{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第三题：神经网络：对数几率回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "实验内容：\n",
    "1. 完成对数几率回归\n",
    "2. 使用梯度下降求解模型参数\n",
    "3. 绘制模型损失值的变化曲线\n",
    "4. 调整学习率和迭代轮数，观察损失值曲线的变化\n",
    "5. 按照给定的学习率和迭代轮数，初始化新的参数，绘制新模型在训练集和测试集上损失值的变化曲线，完成表格内精度的填写"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对数几率回归，二分类问题的分类算法，属于线性模型中的一种，我们可以将其抽象为最简单的神经网络。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://davidham3.github.io/blog/2018/09/11/logistic-regression/Fig1.png\" ,width=300>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "只有一个输入层和一个输出层，还有一个激活函数，$\\rm sigmoid$，简记为$\\sigma$。  \n",
    "我们设输入为$X \\in \\mathbb{R}^{n \\times m}$，输入层到输出层的权重为$W \\in \\mathbb{R}^{m}$，偏置$b \\in \\mathbb{R}$。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 激活函数\n",
    "\n",
    "$$\n",
    "\\mathrm{sigmoid}(x) = \\frac{1}{1 + e^{-x}}\n",
    "$$\n",
    "\n",
    "这个激活函数，会将输出层的神经元的输出值转换为一个 $(0, 1)$ 区间内的数。\n",
    "\n",
    "因为是二分类问题，我们设类别为0和1，我们将输出值大于0.5的样本分为1类，输出值小于0.5的类分为0类。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 前向传播\n",
    "\n",
    "$$\n",
    "Z = XW + b\\\\\n",
    "\\hat{y} = \\sigma(Z)\n",
    "$$\n",
    "\n",
    "其中，$O \\in \\mathbb{R}^{n}$为输出层的结果，$\\sigma$为$\\rm sigmoid$激活函数。\n",
    "\n",
    "**注意：这里我们其实是做了广播，将$b$复制了$n-1$份后拼接成了维数为$n$的向量。**\n",
    "\n",
    "所以对数几率回归就可以写为：\n",
    "\n",
    "$$\n",
    "\\hat{y} = \\frac{1}{1 + e^{-XW + b}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 损失函数\n",
    "\n",
    "使用对数损失函数，因为对数损失函数较其他损失函数有更好的性质，感兴趣的同学可以去查相关的资料。 \n",
    "\n",
    "针对二分类问题的对数损失函数：\n",
    "\n",
    "$$\n",
    "\\mathrm{loss}(y, \\hat{y}) = - y \\log{\\hat{y}} - (1 - y) \\log{(1 - \\hat{y})}\n",
    "$$\n",
    "\n",
    "在这个对数几率回归中，我们的损失函数对所有样本取个平均值：\n",
    "\n",
    "$$\n",
    "\\mathrm{loss}(y, \\hat{y}) = - \\frac{1}{n} \\sum^n_{i = 1}[y_i \\log{\\hat{y_i}} + (1 - y_i) \\log{(1 - \\hat{y_i})}]\n",
    "$$\n",
    "\n",
    "**注意，这里我们的提到的$\\log$均为$\\ln$，在numpy中为**`np.log`。\n",
    "\n",
    "因为我们的类别只有0和1，所以在这个对数损失函数中，要么前一项为0，要么后一项为0。\n",
    "\n",
    "如果当前样本的类别为0，那么前一项就为0，损失函数变为 $- \\log{(1 - \\hat{y})}$ ，因为我们的预测值 $0 < \\hat{y} < 1$ ，所以 $0 < 1 - \\hat{y} < 1$ ，$- \\log{(1 - \\hat{y})} > 0$ ，为了降低损失值，模型需要让预测值 $\\hat{y}$不断地趋于0。\n",
    "\n",
    "同理，如果当前样本的类别为1，那么降低损失值就可以使模型的预测值趋于1。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 参数更新\n",
    "\n",
    "求得损失函数对参数的偏导数后，我们就可以使用**梯度下降**进行参数更新：\n",
    "\n",
    "$$\n",
    "W := W - \\alpha \\frac{\\partial \\mathrm{loss}}{\\partial W}\\\\\n",
    "b := b - \\alpha \\frac{\\partial \\mathrm{loss}}{\\partial b}\n",
    "$$\n",
    "\n",
    "其中，$\\alpha$ 是学习率，一般设置为0.1，0.01等。\n",
    "\n",
    "经过**一定次数**的迭代后，参数会收敛至最优点。这种基于梯度的优化算法很常用，训练神经网络主要使用这类优化算法。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 反向传播\n",
    "\n",
    "我们使用梯度下降更新参数$W$和$b$。为此需要求得损失函数对参数$W$和$b$的偏导数，根据链式法则有：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial \\mathrm{loss}}{\\partial W} &= \\frac{\\partial \\mathrm{loss}}{\\partial \\hat{y}} \\frac{\\partial \\hat{y}}{\\partial Z} \\frac{\\partial Z}{\\partial W}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "这里我们一项一项求，先求第一项：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial \\mathrm{loss}}{\\partial \\hat{y}} = - \\frac{1}{n} \\sum^n_{i = 1} [\\frac{y}{\\hat{y}} - \\frac{1 - y}{1 - \\hat{y}}]\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "第二项：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial \\hat{y}}{\\partial Z} & = \\frac{\\partial (\\frac{1}{1 + e^{-Z}})}{\\partial Z}\\\\\n",
    "& = \\frac{e^{-Z}}{(1 + e^{-Z})^2}\\\\\n",
    "& = \\frac{e^{-Z}}{(1 + e^{-Z})} \\frac{1}{(1 + e^{-Z})}\\\\\n",
    "& = \\frac{e^{-Z}}{(1 + e^{-Z})} (1 - \\frac{e^{-Z}}{(1 + e^{-Z})})\\\\\n",
    "& = \\sigma(Z)(1 - \\sigma(Z))\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "第三项：\n",
    "\n",
    "$$\n",
    "\\frac{\\partial Z}{\\partial W} = X^{\\mathrm{T}}\n",
    "$$\n",
    "\n",
    "综上：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial \\mathrm{loss}}{\\partial W} &= \\frac{\\partial \\mathrm{loss}}{\\partial \\hat{y}} \\frac{\\partial \\hat{y}}{\\partial Z} \\frac{\\partial Z}{\\partial W}\\\\\n",
    "&= - \\frac{1}{n} \\sum^n_{i = 1} [\\frac{y_i}{\\hat{y_i}} - \\frac{1 - y_i}{1 - \\hat{y_i}}] [\\sigma(Z_i)(1 - \\sigma(Z_i))] {X_i}^{\\mathrm{T}}\\\\\n",
    "&= - \\frac{1}{n} \\sum^n_{i = 1} [\\frac{y_i}{\\hat{y_i}} - \\frac{1 - y_i}{1 - \\hat{y_i}}] [\\hat{y_i}(1 - \\hat{y_i})] {X_i}^{\\mathrm{T}}\\\\\n",
    "&= - \\frac{1}{n} \\sum^n_{i = 1} [y_i(1 - \\hat{y_i}) - \\hat{y_i}(1 - y_i)] {X_i}^{\\mathrm{T}}\\\\\n",
    "&= - \\frac{1}{n} \\sum^n_{i = 1} (y_i - y_i \\hat{y_i} - \\hat{y_i} + y_i \\hat{y_i}) {X_i}^{\\mathrm{T}}\\\\\n",
    "&= - \\frac{1}{n} \\sum^n_{i = 1} (y_i - \\hat{y_i}) {X_i}^{\\mathrm{T}}\\\\\n",
    "&= \\frac{1}{n} [X^{\\mathrm{T}}(\\hat{y} - y)]\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "同理，求$\\rm loss$对$b$的偏导数：\n",
    "\n",
    "**注意，由于$b$是被广播成$n \\times K$的矩阵，因此实际上$b$对每个样本的损失都有贡献，因此对其求偏导时，要把$n$个样本对它的偏导数加和。**\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial \\mathrm{loss}}{\\partial b} &= \\frac{\\partial \\mathrm{loss}}{\\partial \\hat{y}} \\frac{\\partial \\hat{y}}{\\partial Z} \\frac{\\partial Z}{\\partial b}\\\\\n",
    "&= - \\frac{1}{n} \\sum^n_{i = 1} [\\frac{y_i}{\\hat{y_i}} - \\frac{1 - y_i}{1 - \\hat{y_i}}] [\\sigma(Z_i)(1 - \\sigma(Z_i))]\\\\\n",
    "&= - \\frac{1}{n} \\sum^n_{i = 1} [\\frac{y_i}{\\hat{y_i}} - \\frac{1 - y_i}{1 - \\hat{y_i}}] [\\hat{y_i}(1 - \\hat{y_i})]\\\\\n",
    "&= - \\frac{1}{n} \\sum^n_{i = 1} [y_i(1 - \\hat{y_i}) - \\hat{y_i}(1 - y_i)]\\\\\n",
    "&= - \\frac{1}{n} \\sum^n_{i = 1} (y_i - y_i \\hat{y_i} - \\hat{y_i} + y_i \\hat{y_i})\\\\\n",
    "&= \\frac{1}{n} \\sum^n_{i = 1} (\\hat{y_i} - y_i)\\\\\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这样，我们就得到了损失函数对参数的偏导数，然后就可以使用梯度下降算法更新参数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. 导入数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from matplotlib.colors import ListedColormap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们生成半月形数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "X, y = make_moons(n_samples = 2000, noise = 0.3, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x21f493c32e0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (6, 6))\n",
    "cm_bright = ListedColormap(['#FF0000', '#0000FF'])\n",
    "plt.scatter(X[:, 0], X[:, 1], c = y, cmap = cm_bright, edgecolors = 'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "选择40%的数据作为测试集，60%作为训练集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "trainX, testX, trainY, testY = train_test_split(X, y, test_size = 0.4, random_state = 32)\n",
    "trainY = trainY\n",
    "testY = testY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1200, 2), (1200,), (800, 2), (800,))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trainX.shape, trainY.shape, testX.shape, testY.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. 数据预处理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用和第一题一样的预处理方式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "import math\n",
    "s = StandardScaler()\n",
    "trainX = s.fit_transform(trainX)\n",
    "testX = s.transform(testX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. 定义神经网络"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 参数初始化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们需要对神经网络的参数进行初始化，这个网络中只有两个参数，一个$W \\in \\mathbb{R}^{m}$，一个$b \\in \\mathbb{R}$。初始化的时候，我们将参数W随机初始化，参数b初始化为0。为什么要对神经网络的参数进行随机初始化，感兴趣的同学可以去查相关的资料。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize(m):\n",
    "    '''\n",
    "    初始化参数W和参数b\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    W: np.ndarray, shape = (m, )，参数W\n",
    "    \n",
    "    b: np.ndarray, shape = (1, )，参数b\n",
    "    \n",
    "    '''\n",
    "    np.random.seed(32)\n",
    "    W = np.random.normal(size = (m, )) * 0.01\n",
    "    b = np.zeros((1, ))\n",
    "    return W, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2,)\n",
      "(1,)\n"
     ]
    }
   ],
   "source": [
    "# 测试样例\n",
    "Wt, bt = initialize(trainX.shape[1])\n",
    "print(Wt.shape) # (2,)\n",
    "print(bt.shape) # (1,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 前向传播"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来我们要定义神经网络前向传播的过程。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "首先计算$Z = XW + b$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_combination(X, W, b):\n",
    "    '''\n",
    "    完成Z = XW + b的计算\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    X: np.ndarray, shape = (n, m)，输入的数据\n",
    "    \n",
    "    W: np.ndarray, shape = (m, )，权重\n",
    "    \n",
    "    b: np.ndarray, shape = (1, )，偏置\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    Z: np.ndarray, shape = (n, )，线性组合后的值\n",
    "    \n",
    "    '''\n",
    "    \n",
    "    # YOUR CODE HERE\n",
    "    Z = np.dot(X,W) + b\n",
    "    \n",
    "    return Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1200,)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 测试样例\n",
    "Wt, bt = initialize(trainX.shape[1])\n",
    "linear_combination(trainX, Wt, bt).shape #(1200,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来实现激活函数$\\rm sigmoid$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_sigmoid(x):\n",
    "    '''\n",
    "    simgoid 1 / (1 + exp(-x))\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    X: np.ndarray, 待激活的值\n",
    "    \n",
    "    '''\n",
    "    # YOUR CODE HERE\n",
    "    activations = 1. / (1 + np.exp(-x))\n",
    "    return activations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49999999939462925"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 测试样例\n",
    "Wt, bt = initialize(trainX.shape[1])\n",
    "Zt = linear_combination(trainX, Wt, bt)\n",
    "my_sigmoid(Zt).mean() # 0.49999"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在实现$\\rm sigmoid$的时候，可能会遇到上溢(overflow)的问题，可以看到$\\rm sigmoid$中有一个指数运算\n",
    "$$\n",
    "\\mathrm{sigmoid}(x) = \\frac{1}{1 + e^{-x}}\n",
    "$$\n",
    "当$x$很大的时候，我们使用`numpy.exp(x)`会直接溢出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-13-f8f49b6c55d5>:1: RuntimeWarning: overflow encountered in exp\n",
      "  np.exp(1e56)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(1e56)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-11-54fee66bb541>:11: RuntimeWarning: overflow encountered in exp\n",
      "  activations = 1. / (1 + np.exp(-x))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_sigmoid(np.array([-1e56]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "虽说程序没有报错，只是抛出了warning，但还是应该解决一下。\n",
    "\n",
    "解决这种问题的方法有很多，比如，我们可以将$\\rm sigmoid$进行变换：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathrm{sigmoid}(x) &= \\frac{1}{1 + e^{-x}}\\\\\n",
    "&= \\frac{e^x}{1 + e^x}\\\\\n",
    "&= \\frac{1}{2} + \\frac{1}{2} \\mathrm{tanh}(\\frac{x}{2})\n",
    "\\end{aligned}$$\n",
    "\n",
    "其中，$\\mathrm{tanh}(x) = \\frac{\\mathrm{sinh}(x)}{\\mathrm{cosh}(x)} = \\frac{e^x - e^{-x}}{e^x + e^{-x}}$\n",
    "\n",
    "转换成这种形式后，我们就可以直接利用`numpy.tanh`完成$\\rm sigmoid$的计算，就不会产生上溢的问题了。\n",
    "\n",
    "除此以外，最好的解决方法是使用scipy中的`expit`函数，完成$\\rm sigmoid$的计算。我们现在做的都是神经网络底层相关的运算，很容易出现数值不稳定性相关的问题，最好的办法就是使用别人已经实现好的函数，这样就能减少我们很多的工作量，同时又快速地完成任务。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import expit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(X):\n",
    "    return expit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 测试样例\n",
    "sigmoid(np.array([-1e56]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来完成整个前向传播的函数，也就是 $Z = XW+b$ 和 $\\hat{y} = \\mathrm{sigmoid}(Z)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward(X, W, b):\n",
    "    '''\n",
    "    完成输入矩阵X到最后激活后的预测值y_pred的计算过程\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    X: np.ndarray, shape = (n, m)，数据，一行一个样本，一列一个特征\n",
    "    \n",
    "    W: np.ndarray, shape = (m, )，权重\n",
    "    \n",
    "    b: np.ndarray, shape = (1, )，偏置\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    y_pred: np.ndarray, shape = (n, )，模型对每个样本的预测值\n",
    "    \n",
    "    '''\n",
    "    # 求Z\n",
    "    Z = np.dot(X,W) + b\n",
    "    \n",
    "    # 求激活后的预测值\n",
    "    y_pred = my_sigmoid(Z)\n",
    "    \n",
    "    return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49999999939462925"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 测试样例\n",
    "Wt, bt = initialize(trainX.shape[1])\n",
    "forward(trainX, Wt, bt).mean() # 0.4999(没有四舍五入)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来完成损失函数的编写，我们使用的是对数损失，这里需要注意的一个问题是：\n",
    "\n",
    "$$\n",
    "\\mathrm{loss}(y, \\hat{y}) = - \\frac{1}{n}[ y \\log{\\hat{y}} + (1 - y) \\log{(1 - \\hat{y})}]\n",
    "$$\n",
    "\n",
    "在这个对数损失中，$\\hat{y}$中不能有$0$和$1$，如果有$0$，那么损失函数中的前半部分，$\\log{0}$就会出错，如果有$1$，那么后半部分$\\log{(1-1)}$就会出错。\n",
    "\n",
    "所以我们要先将$\\hat{y}$中的$0$和$1$改变一下，把$0$变成一个比较小但是大于$0$的数，把$1$变成小于$1$但是足够大的数。使用`numpy.clip`函数就可以作到这点。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logloss(y_true, y_pred):\n",
    "    '''\n",
    "    给定真值y，预测值y_hat，计算对数损失并返回\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    y_true: np.ndarray, shape = (n, ), 真值\n",
    "    \n",
    "    y_pred: np.ndarray, shape = (n, )，预测值\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    loss: float, 损失值\n",
    "    \n",
    "    '''\n",
    "    # 下面这句话会把y_pred里面小于1e-10的数变成1e-10，大于1 - 1e-10的数变成1 - 1e-10\n",
    "    y_hat = np.clip(y_pred, 1e-10, 1 - 1e-10)\n",
    "    \n",
    "    # 求解对数损失\n",
    "    loss = -np.mean(y_true * np.log(y_pred) + (1 - y_true) * np.log(1 - y_pred))                                     # YOUR CODE HERE\n",
    "    \n",
    "    return loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6974035295177312"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 测试样例\n",
    "Wt, bt = initialize(trainX.shape[1])\n",
    "logloss(trainY, forward(trainX, Wt, bt)) # 0.69740"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 反向传播"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们接下来要完成损失函数对参数的偏导数的计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_gradient(y_true, y_pred, X):\n",
    "    '''\n",
    "    给定预测值y_pred，真值y_true，传入的输入数据X，计算损失函数对参数W的偏导数的导数值dW，以及对b的偏导数的导数值db\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    y_true: np.ndarray, shape = (n, ), 真值\n",
    "    \n",
    "    y_pred: np.ndarray, shape = (n, )，预测值\n",
    "    \n",
    "    X: np.ndarray, shape = (n, m)，数据，一行一个样本，一列一个特征\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    dW: np.ndarray, shape = (m, ), 损失函数对参数W的偏导数\n",
    "    \n",
    "    db: float, 损失函数对参数b的偏导数\n",
    "    \n",
    "    '''\n",
    "    # 求损失函数对参数W的偏导数的导数值\n",
    "    \n",
    "    # 计算W的梯度\n",
    "    # YOUR CODE HERE\n",
    "    dW = np.dot(X.T,(y_pred - y_true)) * 1 / y_true.shape\n",
    "    \n",
    "    # 求损失函数对参数b的偏导数的导数值\n",
    "    db = sum(y_pred - y_true) * 1 / y_true.shape\n",
    "    \n",
    "    return dW, db"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2,)\n",
      "0.0462594198167427\n",
      "[0.01]\n"
     ]
    }
   ],
   "source": [
    "# 测试样例\n",
    "Wt, bt = initialize(trainX.shape[1])\n",
    "dWt, dbt = compute_gradient(trainY, forward(trainX, Wt, bt), trainX)\n",
    "print(dWt.shape) # (2, )\n",
    "print(dWt.sum()) # 0.04625\n",
    "print(dbt)       # 0.00999"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4 参数更新\n",
    "给定学习率，结合上一步求出的偏导数，完成梯度下降的更新公式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update(W, b, dW, db, learning_rate):\n",
    "    '''\n",
    "    梯度下降，给定参数W，参数b，以及损失函数对他们的偏导数，使用梯度下降更新参数W和参数b\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    W: np.ndarray, shape = (m, )，参数W\n",
    "    \n",
    "    b: np.ndarray, shape = (1, )，参数b\n",
    "    \n",
    "    dW: np.ndarray, shape = (m, ), 损失函数对参数W的偏导数\n",
    "    \n",
    "    db: float, 损失函数对参数b的偏导数\n",
    "    \n",
    "    learning_rate, float，学习率\n",
    "    \n",
    "    '''\n",
    "    # 对参数W进行更新\n",
    "    W -= learning_rate * dW\n",
    "    \n",
    "    # 对参数b进行更新\n",
    "    b -= learning_rate * db"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.00348894  0.00983703]\n",
      "[0.]\n",
      "\n",
      "[-0.28650366  0.33276308]\n",
      "[0.01]\n",
      "\n",
      "[-0.00062391  0.0065094 ]\n",
      "[-9.99999939e-05]\n"
     ]
    }
   ],
   "source": [
    "# 测试样例\n",
    "Wt, bt = initialize(trainX.shape[1])\n",
    "print(Wt)  # [-0.00348894  0.00983703]\n",
    "print(bt)  # [ 0.]\n",
    "print()\n",
    "\n",
    "dWt, dbt = compute_gradient(trainY, forward(trainX, Wt, bt), trainX)\n",
    "print(dWt) # [-0.28650366  0.33276308]\n",
    "print(dbt) # 0.00999999939463\n",
    "print()\n",
    "\n",
    "update(Wt, bt, dWt, dbt, 0.01)\n",
    "print(Wt)  # [-0.00062391  0.0065094 ]\n",
    "print(bt)  # [ -9.99999939e-05]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们来完成整个反向传播和更新参数的函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def backward(y_true, y_pred, X, W, b, learning_rate):\n",
    "    '''\n",
    "    反向传播，包含了计算损失函数对各个参数的偏导数的过程，以及梯度下降更新参数的过程\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    y_true: np.ndarray, shape = (n, ), 真值\n",
    "    \n",
    "    y_pred: np.ndarray, shape = (n, )，预测值\n",
    "    \n",
    "    X: np.ndarray, shape = (n, m)，数据，一行一个样本，一列一个特征\n",
    "    \n",
    "    W: np.ndarray, shape = (m, )，参数W\n",
    "    \n",
    "    b: np.ndarray, shape = (1, )，参数b\n",
    "    \n",
    "    dW: np.ndarray, shape = (m, ), 损失函数对参数W的偏导数\n",
    "    \n",
    "    db: float, 损失函数对参数b的偏导数\n",
    "    \n",
    "    learning_rate, float，学习率\n",
    "    \n",
    "    '''\n",
    "    # 求参数W和参数b的梯度\n",
    "    dW, db = compute_gradient(y_true, y_pred, X)\n",
    "    \n",
    "    # 梯度下降\n",
    "    update(W, b, dW, db, learning_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6974035295177312\n",
      "0.6954776267143474\n"
     ]
    }
   ],
   "source": [
    "# 测试样例\n",
    "Wt, bt = initialize(trainX.shape[1])\n",
    "y_predt = forward(trainX, Wt, bt)\n",
    "loss_1 = logloss(trainY, y_predt)\n",
    "print(loss_1)                             # 0.697403529518\n",
    "\n",
    "backward(trainY, y_predt, trainX, Wt, bt, 0.01)\n",
    "\n",
    "y_predt = forward(trainX, Wt, bt)\n",
    "loss_2 = logloss(trainY, y_predt)\n",
    "print(loss_2)                             # 0.695477626714"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. 训练函数的编写"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们已经实现了完成训练需要的子函数，接下来就是组装了"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(trainX, trainY, testX, testY, W, b, epochs, learning_rate = 0.01, verbose = False):\n",
    "    '''\n",
    "    训练，我们要迭代epochs次，每次迭代的过程中，做一次前向传播和一次反向传播\n",
    "    同时记录训练集和测试集上的损失值，后面画图用\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    trainX: np.ndarray, shape = (n, m), 训练集\n",
    "    \n",
    "    trainY: np.ndarray, shape = (n, ), 训练集标记\n",
    "    \n",
    "    testX: np.ndarray, shape = (n_test, m)，测试集\n",
    "    \n",
    "    testY: np.ndarray, shape = (n_test, )，测试集的标记\n",
    "    \n",
    "    W: np.ndarray, shape = (m, )，参数W\n",
    "    \n",
    "    b: np.ndarray, shape = (1, )，参数b\n",
    "    \n",
    "    epochs: int, 要迭代的轮数\n",
    "    \n",
    "    learning_rate: float, default 0.01，学习率\n",
    "    \n",
    "    verbose: boolean, default False，是否打印损失值\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    training_loss_list: list(float)，每迭代一次之后，训练集上的损失值\n",
    "    \n",
    "    testing_loss_list: list(float)，每迭代一次之后，测试集上的损失值\n",
    "    \n",
    "    '''\n",
    "    \n",
    "    training_loss_list = []\n",
    "    testing_loss_list = []\n",
    "    \n",
    "    for i in range(epochs):\n",
    "        \n",
    "        # 计算训练集前向传播得到的预测值\n",
    "        train_y_pred = forward(trainX,W,b)\n",
    "        # YOUR CODE HERE\n",
    "\n",
    "        # 计算当前训练集的损失值\n",
    "        training_loss = logloss(trainY, train_y_pred)\n",
    "        # YOUR CODE HERE\n",
    "        \n",
    "        # 计算测试集前向传播得到的预测值\n",
    "        test_y_predt = forward(testX,W,b)\n",
    "        # YOUR CODE HERE\n",
    "        \n",
    "        # 计算当前测试集的损失值\n",
    "        testing_loss = logloss(testY, test_y_predt)\n",
    "        # YOUR CODE HERE\n",
    "        \n",
    "        if verbose == True:\n",
    "            print('epoch %s, training loss:%s'%(i + 1, training_loss))\n",
    "            print('epoch %s, testing loss:%s'%(i + 1, testing_loss))\n",
    "            print()\n",
    "        \n",
    "        # 保存损失值\n",
    "        training_loss_list.append(training_loss)\n",
    "        testing_loss_list.append(testing_loss)\n",
    "        \n",
    "        # 反向传播更新参数\n",
    "        # YOUR CODE HERE\n",
    "        backward(trainY, train_y_pred, trainX, W, b, learning_rate)\n",
    "\n",
    "    \n",
    "    return training_loss_list, testing_loss_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.6974035295177312, 0.6784372906072572]\n",
      "[0.6974366128610399, 0.6788012623558839]\n"
     ]
    }
   ],
   "source": [
    "# 测试样例\n",
    "Wt, bt = initialize(trainX.shape[1])\n",
    "training_loss_list, testing_loss_list = train(trainX, trainY, testX, testY, Wt, bt, 2, 0.1)\n",
    "print(training_loss_list)  # [0.69740352951773121, 0.67843729060725722]\n",
    "print(testing_loss_list)   # [0.69743661286103986, 0.67880126235588389]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. 绘制模型损失值变化曲线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_loss_curve(training_loss_list, testing_loss_list):\n",
    "    '''\n",
    "    绘制损失值变化曲线\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    training_loss_list: list(float)，每迭代一次之后，训练集上的损失值\n",
    "    \n",
    "    testing_loss_list: list(float)，每迭代一次之后，测试集上的损失值\n",
    "    \n",
    "    '''\n",
    "    plt.figure(figsize = (10, 6))\n",
    "    plt.plot(training_loss_list, label = 'training loss')\n",
    "    plt.plot(testing_loss_list, label = 'testing loss')\n",
    "    plt.xlabel('epoch')\n",
    "    plt.ylabel('loss')\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. 预测"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来编写一个预测的函数，事实上，$\\rm sigmoid$输出的是当前这个样本为正例的概率，也就是说，这个输出值是一个0到1的值，一般我们将大于0.5的值变成1，小于0.5的值变成0，也就是说，如果当前输出的概率值大于0.5，那我们认为这个样本的类别就是1，否则就是0，这样输出的就是类标了。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(X, W, b):\n",
    "    '''\n",
    "    预测，调用forward函数完成神经网络对输入X的计算，然后完成类别的划分，大于0.5的变为1，小于等于0.5的变为0\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    X: np.ndarray, shape = (n, m), 训练集\n",
    "    \n",
    "    W: np.ndarray, shape = (m, 1)，参数W\n",
    "    \n",
    "    b: np.ndarray, shape = (1, )，参数b\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    prediction: np.ndarray, shape = (n, 1)，预测的标记\n",
    "    \n",
    "    '''\n",
    "\n",
    "    prediction = (forward(X, W, b) > 0.5).astype('int')\n",
    " \n",
    "    return prediction\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1625"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 测试样例\n",
    "from sklearn.metrics import accuracy_score\n",
    "Wt, bt = initialize(trainX.shape[1])\n",
    "predictiont = predict(testX, Wt, bt)\n",
    "accuracy_score(testY, predictiont)  # 0.16250000000000001"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. 训练一个神经网络"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们的学习率是0.01，迭代200轮"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "W, b = initialize(trainX.shape[1])\n",
    "training_loss_list, testing_loss_list = train(trainX, trainY, testX, testY, W, b, 200, 0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "计算测试集精度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.83625"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction = predict(testX, W, b)\n",
    "accuracy_score(testY, prediction)  # 0.83625000000000005"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绘制损失值变化曲线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_loss_curve(training_loss_list, testing_loss_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 课后部分：初始化新的参数，学习率和迭代轮数按下表设置，绘制其训练集和测试集损失值的变化曲线，完成表格内精度的填写，并结合参数学习率对曲线变化及训练过程进行分析"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### 双击此处填写\n",
    "\n",
    "学习率|迭代轮数|测试集精度\n",
    "-|-|-\n",
    "0.0001|200|\n",
    "0.1|1000|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'learning rate:0.0001 epoch:200')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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QvXr1YtCgQaxdu5bTp09z8uRJOnfuzJgxY/7cWv437NVfWSgpJZW7ZqVxZ/2PuL3hz/j89AJ80B5q3eGs2BUs5+0QjTHGmGynaNGiNG/enLCwMDp16kSXLl0uOh4ZGcnEiROpXbs2VatWpUmTJlc8hhEjRtCjRw9mzJhB69atKV26NMHBwR77h4eH06dPHxo1agTAAw88QL169Zg7dy6DBw/Gx8cHf39/JkyYQHx8PDfffDOJiYmoKm+//fa/jlf+7pLitaRBgwa6Zs2aLJv/j5OJDPhsLdG7j1O7XEFeiAyh3p6PYPm7gEDzgdD8MciTL7OpjDHGmKtm06ZNVK9e3dtheFVSUhK+vr74+fmxYsUKHnrooSuykna5Mvo7EJFoVW2QUX/bcs1CpQoG8mX/poz5T10Onkqk2/vreeLwjRzuswyqdoLFr8G7DeC3zyEtzdvhGmOMMcZlz549NGzYkDp16jBw4EAmT57s7ZAuyVbosnCFzl1CUgrjo7YxeclO/HyFAW2u54GKBwmY/wwcWAdlG0Cn16Bchom3McYYc9XYCp332QpdNpUvwI/BHaux4MnWtLi+GG/M3UL7L5OZ13waevN7cHIvvH8DfP0gnNzn7XCNMcYYk4NYQneVVSgaxKTeDfjk/kbk8fPhwU9/pffaymzvvhhaPgUx38K4BhD1GiSf8Xa4xhhjjMkBLKHzkpaVi/PjYy0ZfmMN1u09QYfxv/LCmds41XcFVO4AUaNgXEP4/UvIxdvixhhjjMmcJXRe5O/rw30tQokaFMGdDcrz0fJdREzewbSQl0i9ZxYEFYGv7ocPOsC+aG+Ha4wxxphsyhK6bKBo/gBeubUWMx9pwXXF8zH069+5aaayusPXcNM4OL4LJreFb/rDqf3eDtcYY4zJUidOnGD8+PH/ePyYMWM4c+ZC2VLnzp2vyPtSd+3aRVhY2L+eJytYQpeNhJUtyOf9mjK2Rz2OJSRzx6RVDNwSxh99lkOLJ2DDV/BufVj8OpzL+PUlxhhjTE53pRO62bNnU6hQoSsRWrZlCV02IyLcVKcMPz3VmoFtr2dOzB+0GRvNu3IXSf1WwvXtYNHLTn3dhq+svs4YY8w1Z8iQIWzfvp26desyePBgAN544w0aNmxI7dq1GTFiBAAJCQl06dKFOnXqEBYWxowZMxg7diz79++nTZs2tGnTBoCQkBCOHDnCrl27qF69On379qVmzZp06NDhz/e7rl69mtq1a9O0aVMGDx6c6UpcYmIi9957L7Vq1aJevXosWrQIgJiYGBo1akTdunWpXbs2sbGxGcZ5pdmrv7KpoDx+PNmhKnc0KM+o2Zt4a/5WZqzJy7Aur9OxUV9kzjPw5X3wyySIfAXKhns7ZGOMMdeiH4fAH79f2TlL1YJOr3o8/Oqrr7Jhw4Y/38wwb948YmNjWbVqFarKTTfdxJIlSzh8+DBlypRh1qxZgPOO14IFCzJ69GgWLVpEsWLF/jJ3bGws06ZNY/Lkydx555189dVX9OrVi3vvvZdJkybRrFkzhgwZkukpvPfeewD8/vvvbN68mQ4dOrB161YmTpzIY489xl133UVycjKpqanMnj37L3FeabZCl82VLxLEhF71+eyBxuTL40f/T9dy14I8bLn5B+g6Fo5th8lt4NuH4dQBb4drjDHGXHHz5s1j3rx51KtXj/DwcDZv3kxsbCy1atViwYIFPP300yxdupSCBQtmOldoaCh169YFoH79+uzatYsTJ04QHx9Ps2bNAOjZs2em8yxbtoy7774bgGrVqlGxYkW2bt1K06ZNGTVqFK+99hq7d+8mb968/yjOv8tW6HKIZtcXY9bAFkz9ZQ+j52+l87jl3N2kAU88sIqCa8bAygnOM+xaPglNB4B/Xm+HbIwx5lpwiZW0q0VVGTp0KP369fvLsejoaGbPns3QoUPp0KEDw4cPv+RcAQEBf37v6+vL2bNn+SdvzfI0pmfPnjRu3JhZs2bRsWNH3n//fdq2bfu34/y7bIUuB/Hz9eGeZiFEDYqgR6PyfLxiFxHvruHT4PtJfegXuK4NLHwJxjWCmG+svs4YY0yOFBwcTHx8/J8/d+zYkSlTpnD69GkA9u3bx6FDh9i/fz9BQUH06tWLQYMGsXbt2gzHZ6Zw4cIEBwezcuVKAKZPn57pmFatWjF16lQAtm7dyp49e6hatSo7duygUqVKDBw4kJtuuonffvvNY5xXkq3Q5UCF8+Vh5C216NmoIi/MjGHYtxuYWroAz3cdS+PG/WDOUPiiD1Ro5tTXlanr7ZCNMcaYy1a0aFGaN29OWFgYnTp14o033mDTpk00bdoUgPz58/Ppp5+ybds2Bg8ejI+PD/7+/kyYMAGABx98kE6dOlG6dOk/b1bIzAcffEDfvn3Jly8fERERmW6LPvzww/Tv359atWrh5+fHRx99REBAADNmzODTTz/F39+fUqVKMXz4cFavXp1hnFeS/JNlxmtFgwYNdM2aNd4O419RVWb//gejZm9i34mzdKldmmciq1B2xxewcCScOQr17oK2wyG4pLfDNcYYkwNk9GL4a93p06fJnz8/4NyUceDAAd555x2vxZPR34GIRKtqg4z625ZrDicidKldmgVPtubxdpVZsPEgN7y9lDEnmpP40Bpo9gisnwHvhsPS0XAu0dshG2OMMdnOrFmzqFu3LmFhYSxdupRhw4Z5O6S/xVbocvgKXXpxx8/wyuzNzPr9AGUL5eWZztXpXCYBmT8ctsyCQhWhw0tQ/SYQ8Xa4xhhjsqHcuEKX3dgKXS5XrnAQ790VzrS+TQgO9GPAZ2vp8fVhNkVMhN7fQZ588Hlv+OhGOLDe2+EaY4wx5gqwhO4a1fS6ovzwaAteuiWMzX/E02XsUp77rRjH7/4JuoyGw5vgv63h+0fh9CFvh2uMMSabyc07eN72T669JXTXMD9fH+5uUpGoQRHc3aQin63aQ8ToZXyccgMpA6Kd59Wt+wzGhsOyMZCS5O2QjTHGZAOBgYEcPXrUkjovUFWOHj1KYGDg3xpnNXTXWA3dpWz5I54XZsawfPtRqpUKZnjXGjQreALmDYOtP0LhEOgwEqrdaPV1xhiTi507d464uDgSE+1GOm8IDAykXLly+Pv7X9R+qRo6S+hyUUIHTuY/N+YPRs7aRNzxs3QKK8UznatT/vhKmPOMsxUb0tJ5fl2pWt4O1xhjjDEudlOE+ZOIEBnmPObkqfZViNpymHajFzN6e1nO3r8YOr8JB2Pgv61g5mNw+rC3QzbGGGNMJmyFLpet0KW3/8RZXvlxMzPX76d0wUCGdq5O18p5kSWvw6pJ4B8ErQZD4/7gl8fb4RpjjDG5lm25emAJ3QWrdh7j+e9j2HjgFI1CijDiphrU9D/o1NfFzoUilZz6uqqdrb7OGGOM8QLbcjWZahRahJmPtmBUt1psO3yaru8u45llSRy75VPo9RX4+MP0nvDxzc6WrDHGGGOyDVuhsxW6vzh55hxjftrKxyt2ky+PL0+0r0KvhmXw//V/EDUKEk9C/T7Q5lnIV8zb4RpjjDG5gtdW6EQkUkS2iMg2ERnioU+EiKwTkRgRWezW/piIbHC1P+7WPsPVf52I7BKRdW7Hhro+a4uIdMzKc7uWFQzyZ0TXmsx5rCV1yhfihZkb6TxuJcuK3AqProVGD0L0/5zn1y0fBynJ3g7ZGGOMydWybIVORHyBrUB7IA5YDfRQ1Y1ufQoBy4FIVd0jIiVU9ZCIhAHTgUZAMjAHeEhVY9N9xlvASVV9UURqANNcY8oAC4AqqprqKUZbocucqjJ/40FGztrEnmNn6FCjJMO61KBC2l6Y+wxsWwBFroOOL0OVSKuvM8YYY7KIt1boGgHbVHWHqibjJGg3p+vTE/haVfcAqOr5d1BVB1aq6hlVTQEWA93cB4qIAHfiJHG45p6uqkmquhPY5orB/AsiQoeapZj3RCsGd6zKsm1HaPf2Yt5cCwl3zIC7vgQfX5jWHT7pBgc3Zj6pMcYYY66orEzoygJ73X6Oc7W5qwIUFpEoEYkWkd6u9g1AKxEpKiJBQGegfLqxLYGDbqt2l/N5iMiDIrJGRNYcPmzPWLtcgf6+DGhzPQufiqBzWCnGLdrGDW8t5tvTNdD+P0Pka7D/V5jYHGY9BQlHvR2yMcYYk2tkZUKX0d5b+v1dP6A+0AXoCDwnIlVUdRPwGjAfZ7t1PZCSbmwPLqzOXe7noaqTVLWBqjYoXrz4ZZ2IuaBUwUDGdK/HVw81pXhwAI/PWMcdk9ewoXwPGPgrNHwA1nwI79aDFeMh9Zy3QzbGGGOueVmZ0MVx8apaOWB/Bn3mqGqCqh4BlgB1AFT1A1UNV9VWwDHgz/o5EfEDbgVm/M3PM1dI/YpF+G5Ac167rRa7jibQddwyhvwYx5FWI+Ghn6FsfZg7FMY3ha1zIRffTW2MMcZktaxM6FYDlUUkVETyAN2B79P1+Q5oKSJ+rq3VxsAmABEp4fpaASd5c1+NawdsVtU4t7bvge4iEiAioUBlYFUWnJdx8fER/tOwAgsHRXB/81C+jI6jzZtRvL8lgHM9voSenwMKn90Jn94GhzZ7O2RjjDHmmpRlCZ3rZoZHgLk4SdrnqhojIv1FpL+rzyacLdXfcJKv91V1g2uKr0RkIzATGKCqx92m787FCR6qGgN8Dmx0zTngUne4miunQKA/w26swZzHWxFeoTAjZ20i8p2lLCYcHloBHV+BfWtgQjOYPRjOHPN2yMYYY8w1xR4sbI8tuaJUlYWbD/HiDxvZffQM7aqXYFiXGoTkTXQeSrxmCgQUgIih0PB+8PX3dsjGGGNMjmDvcvXAErqsk5SSypRluxi3MJZzqcr9LUMZ0OZ68p/Y6tTW7YiCYlWg4yio3N7b4RpjjDHZnr3L1Vx1AX6+PBRxHYsGRXBjndJMiNpO2zej+HpfAdLu+gZ6TIe0VJh6O3x6Oxze4u2QjTHGmBzLVuhshe6qWLvnOC98H8P6uJPUq1CI57vWpE7pIFg1CRa/DsmnoVFfaP00BBXxdrjGGGNMtmNbrh5YQnd1paUpX62N47U5WzhyOok76pdjcGRVSvichkUvQ/RHEFgQIp6BBveBr5+3QzbGGGOyDUvoPLCEzjviE88xbuE2pvy8kwA/XwbecD19moWS58hGp75u5xIoXs15P+z17bwdrjHGGJMtWA2dyVaCA/0Z2rk6cx9vRaPQIoyavZnIMUtYdKIE9P4eun8GKUnOs+um3glHYjOf1BhjjMnFLKEzXlOpeH6m9GnIh30aAnDvR6u5739r2FksAgb8Au1fgj0rYHwTmDMUzh6/9ITGGGNMLmVbrrblmi0kp6Tx0fKdjP1pG0kpqdzXPJRH2l5PcMoJWDQSov8HeQtDm2eg/r1WX2eMMSbXsRo6Dyyhy34OxSfyxpwtfBEdR7H8ATwdWZXbwsvhc2iDs0q3aykUrw6Ro+C6tt4O1xhjjLlqrIbO5BglggN54446fDegOeWL5GXwl7/RbcJyfk0uB/fMhP98Ciln4ZNu8Fl3OLLN2yEbY4wxXmcrdLZCl22lpSnfrtvHqz9u5lB8EreGl2VIZDVKBAmsnABL3oSURGjcD1oNhryFvB2yMcYYk2Vsy9UDS+hyhtNJKby3aBsfLN2Jv6/wSNvK3NcihICzR5z6urWfOA8jbvMshN9j9XXGGGOuSZbQeWAJXc6y60gCI2dtYsGmg4QUDWJYlxrcUL0E8sdvTn3d7p+hRE2nvq5ShLfDNcYYY64oq6Ez14SQYvl4/54G/O++Rvj6CA98vIY+H65mm+910GcW3PkxJMfDxzfDtJ5wdLu3QzbGGGOuCluhsxW6HOlcahr/W76LdxbEcvZcKn2ahTCwXWUK+KbCyvGw9C3n4cRN+jv1dYEFvR2yMcYY86/YlqsHltDlfEdOJ/Hm3C3MWLOXovnyMLhjVe6oXx6fhIOw8CX4dSoEFYW2wyC8N/j4ejtkY4wx5h+xhM4DS+iuHb/HneT5mTFE7z5OrbIFef6mGtSvWAT2/+rU1+1ZASXDIPIVCG3l7XCNMcaYv81q6Mw1r1a5gnzZvynvdK/L4fgkbpuwgsen/8of+arDvT/CHR9B4in4X1eYfhcc2+HtkOBWsR4AACAASURBVI0xxpgrxlbobIXumpOQlMKEqO1MWroDPx9hQJvrub9FKIEkw4r3YOloSDsHTR6CloMgsIC3QzbGGGMyZVuuHlhCd23bc/QMI2dtZN7Gg1QoEsSzXarToUZJJP4Pp75u3VTIVxzaPgf1ell9nTHGmGzNtlxNrlShaBCTejfg0/sbE+DnQ79Pouk9ZRWxZ/PDLeOh7yIoch3MHAiTWsOuZd4O2RhjjPlHbIXOVuhyhXOpaXy6cjdvz99KQnIqvZtW5PF2VSgY6AcxX8P8EXByL1S/CTq8BIVDvB2yMcYYcxHbcvXAErrc5+jpJN6av5Vpq/ZQOCgPgzpU5T8Ny+ObmgjLx8Gy0ZCWAk0HQMunICDY2yEbY4wxgCV0HllCl3vF7D/JC99vZNWuY9QsU4Dnb6pJw5AicGo//PQirJ8G+UrADcOh7l3gY9UJxhhjvMtq6IxJp2aZgszo14R3e9TjeEIyd0xcwaPTfmV/WmHoNhEeWOhsu37/iFNft3u5t0M2xhhjPLIVOluhy/XOJqcyYfF2/rt4Oz4iPBxxHX1bVSLQzwc2fAXzh8OpfVDjFmj/IhSu6O2QjTHG5EK25eqBJXTG3d5jZxg1exM/bviDcoXzMqxLdTrWLIWcOwvL34Vlb4OmQbNHoMWTEJDf2yEbY4zJRSyh88ASOpOR5duP8ML3G9lyMJ5m1xVlRNeaVC0VDCf3wYLn4ffPIX9JuGEE1Olh9XXGGGOuCkvoPLCEzniSkprGZ6v28Na8rZxOSqFX4wo80b4KhYLywN7VMGcI7FsDpetC5KtQsam3QzbGGHON89pNESISKSJbRGSbiAzx0CdCRNaJSIyILHZrf0xENrjaH0835lHXvDEi8rqrLUREzrrmWiciE7Py3My1zc/Xh95NQ4gaFEHPRhX4ZOVu2rwZxScrd5NatgHcPx9unQynD8GHkfDFvXBij7fDNsYYk0tl2QqdiPgCW4H2QBywGuihqhvd+hQClgORqrpHREqo6iERCQOmA42AZGAO8JCqxopIG+BZoIuqJrmNCQF+UNWwy43RVujM5dp04BQvzIxh5Y5jVCsVzPM31aRJpaKQnAA/j4Wf3wEUmj0KzR+3+jpjjDFXnLdW6BoB21R1h6om4yRoN6fr0xP4WlX3AKjqIVd7dWClqp5R1RRgMdDNdewh4FVVTUo3xpgsU710Aab1bcL4u8KJT0yh+6SVDJi6lrgEgTZD4dE1UL0rLHkDxjWAddMgLc3bYRtjjMklsjKhKwvsdfs5ztXmrgpQWESiRCRaRHq72jcArUSkqIgEAZ2B8m5jWorILyKyWEQaus0XKiK/utpbXvlTMrmZiNC5Vml+eqo1T7Srwk+bD3LDW4sZs2ArZ/OWhtved7Zig0vDt/3h/Rtgzy/eDtsYY0wukJUJnWTQln5/1w+oD3QBOgLPiUgVVd0EvAbMx9luXQ+kuI0pDDQBBgOfi4gAB4AKqloPeBL4TEQK/CUokQdFZI2IrDl8+PC/PUeTCwX6+/JYu8r89FQE7WqUZMyCWNqNXsys3w6g5RrCAz9Bt/9C/AGY0gG+vB9O7M18YmOMMeYfysqELo4Lq2oA5YD9GfSZo6oJqnoEWALUAVDVD1Q1XFVbAceAWLcxX6tjFZAGFFPVJFU96hobDWzHWc27iKpOUtUGqtqgePHiV+xkTe5TtlBe3usZzvQHm1Agrz8DPltL90kr2XTwNNTpDo+sgVb/B5t/gHENYdEop+bOGGOMucKyMqFbDVQWkVARyQN0B75P1+c7nO1TP9fWamNgE4CIlHB9rQDcCkxzjfkWaOs6VgXIAxwRkeKuGzEQkUpAZWBHFp6fMQA0qVSUHx5twchbwth6MJ4uY5cy7NvfOZ6SB9o+C4+shqqdYPFr8G59WD/d6uuMMcZcUVmW0LluZngEmIuTpH2uqjEi0l9E+rv6bMLZUv0NWAW8r6obXFN8JSIbgZnAAFU97mqfAlQSkQ04N1rco86tuq2A30RkPfAl0F9Vj2XV+RnjztdH6NWkIosGRdC7aQjTVu0l4s0o/rd8FynB5eCOD+G+uU593Tf9rL7OGGPMFWUPFrbHlpgssOWPeF78IYaftx2laslgRnStQbPrizkrc79/7rxxIv4AhN0O7Z6HQuUzmdEYY0xuZ2+K8MASOpOVVJW5MQcZOWsjccfPElmzFM92qU75IkGQdNp5dt3ysU5ne36dMcaYTFhC54EldOZqSDyXyvtLd/Deou2kqtKvVSUeiriOoDx+zt2vP70Av3/hbMfeMAJq/8feD2uMMeYvLKHzwBI6czUdOHmWV3/czHfr9lOqQCBDO1fjpjplEBHYu8r1fthoKFPPeT9shSbeDtkYY0w24rV3uRpjLihdMC/vdK/Hl/2bUjw4gMemr+P2iSv4Pe4klG8E9y+AbpMg/iBM6WjvhzXGGHPZbIXOVuiMF6SlKV9Gx/H63M0cTUjmzvrlGdSxKsWDAy5+P6ymOfV1LZ6w+jpjjMnlbMvVA0vojLedSjzHuIXb+PDnnQT6+TLwhsrc0yyEPH4+cDIOFrzg3BWbvxTcMBzq9LD6OmOMyaUsofPAEjqTXew4fJqRszaxcPMhQovl47kbq9O2Wknn4N7Vrvq6NVC6LkS+AhWbeTdgY4wxV53V0BmTzVUqnp8pfRry4b0NEeC+j9bQ58NVbD98Gso3hPvnw63vQ8Jh+LATfH4PHN/t7bCNMcZkE7ZCZyt0JptJTknj4xW7eGdBLGfPpdKnWQgD21WmQKA/JJ+B5e/Cz2MgLRWaPeKqrwv2dtjGGGOymG25emAJncnODscn8da8LcxYs5ei+fIwuGNVbq9fHl8fgZP7nOfX/TYD8pd01df1tPo6Y4y5hllC54EldCYn+D3uJC/MjGHN7uOElS3A811r0iCkiHMwbo1TXxe3GkrVdp5fF9LcuwEbY4zJElZDZ0wOVqtcQb7o35R3utflSHwyt09cwcBpv3Lg5Fko18Cpr7vtAzhzDD7qDJ/3huO7vB22McaYq8hW6GyFzuQgZ5JTmBi1nYlLduArwsMR19G3VSUC/X2d+roV42DZ25CWAk0HQIsnIbCAt8M2xhhzBdiWqweW0Jmcau+xM4yavYkfN/xBucJ5ebZzdSLDSjmvETu1H356EdZPg3wl4IbnoO5d4OPr7bCNMcb8C5bQeWAJncnplm8/woszN7L5j3iaVirK8K41qF7atSK3LxrmDIW9v0CpWq76uhbeDdgYY8w/ZgmdB5bQmWtBSmoa01bv5a15Wzh19hx3Na7Ik+2rUDhfHlCFmK9h/gg4uReqd4X2L0GRUG+HbYwx5m+yhM4DS+jMteTEmWTenr+VT3/ZQ/4AP55sX4W7GlfAz9cHzp116uuWvg1p56DJQ9BykNXXGWNMDmIJnQeW0Jlr0ZY/4nnxhxh+3naUKiXzM6JrTZpfX8w5eOoALHwJ1k2FfMWh7TCod7fV1xljTA5gCZ0HltCZa5WqMm/jQUbO2sjeY2fpUKMkw7rUoELRIKfDvrUw9xnYswJK1oLIURDayrtBG2OMuSRL6DywhM5c6xLPpfLBsp28t2gbKanKAy1DGdDmevIF+Dn1dRu/hXnD4eQeqHYjdHgJilTydtjGGGMyYAmdB5bQmdzij5OJvD5nM1//uo8SwQEM6VSNW+qWxcdHXPV178HS0ZCa7NTXtRoEgQW9HbYxxhg3ltB5YAmdyW2idx/nxZkxrI87Sb0KhXi+a03qlC/kHIz/w6mv+3UqBBV16uvCe1t9nTHGZBOW0HlgCZ3JjdLSlK/WxvHanC0cOZ3E7fXL8X+RVSkRHOh02P8rzHkG9iyHkmHQcRRUau3doI0xxlhC54kldCY3i088x7hF25iybCcBfr482vZ6+jQPIcDP11Vf9x3Mfw5O7IGqXZz6uqLXeTtsY4zJtSyh88ASOmNg55EERv6wkZ82HyKkaBDP3ViDttVKOK8RO5cIK8fD0rcgJQka94NWgyFvIW+HbYwxuY4ldB5YQmfMBVFbDvHSDxvZfjiBVlWKM/zGGlxfIr9zMP6gq77uUwgqAm2ehfB7wNfPu0EbY0wuYgmdB5bQGXOxc6lpfLxiN2MWbOVscir3NAth4A2VKZjX3+lwYL3zftjdP0OJGhD5ClSK8GbIxhiTa1hC54EldMZk7MjpJN6at4Xpq/dSJCgPgzpW5c4G5fH1Eae+btNMmDcMTuyGqp2hw0irrzPGmCxmCZ0HltAZc2kb9p3khZkxrN51nJplCjCia00ahRZxDp5LhF8mwJK3ICXR6uuMMSaLWULngSV0xmROVfnhtwO8MnsT+08m0rVOGYZ2qkaZQnmdDvEHYdFIWPsJ5C0MbZ+F8D5WX2eMMVfYpRI6nyz+4EgR2SIi20RkiIc+ESKyTkRiRGSxW/tjIrLB1f54ujGPuuaNEZHX3dqHuj5ri4h0zLozMyb3EBG61inDT09F8NgNlZkX8wdt34rinQWxnE1OheCScNO70G8JlKwJs56CiS1g+0Jvh26MMblGlq3QiYgvsBVoD8QBq4EeqrrRrU8hYDkQqap7RKSEqh4SkTBgOtAISAbmAA+paqyItAGeBbqoapLbmBrANNeYMsACoIqqpnqK0VbojPn74o6f4ZUfNzPrtwOULZSXoZ2r0aVWaecxJ6qweZZTX3d8J1SJdOrrilX2dtjGGJPjeWuFrhGwTVV3qGoyToJ2c7o+PYGvVXUPgKoecrVXB1aq6hlVTQEWA91cxx4CXlXVpHRjbgamq2qSqu4EtrliMMZcQeUKB/Fez3CmP9iEAnn9eeSzX+k+aSUb958CEah+Iwz4Bdq/CLt+hvFNnDtjzx73dujGGHPNysqEriyw1+3nOFebuypAYRGJEpFoEentat8AtBKRoiISBHQGyruNaSkiv4jIYhFp+Dc+DxF5UETWiMiaw4cP/6sTNCY3a1KpKD882oKXu4Wx9WA8N767lGe++Z1jCcngFwDNH4OBa6FeL/hlIowNh1WTITXF26EbY8w1JysTOsmgLf3+rh9QH+gCdASeE5EqqroJeA2Yj7Pduh5IcRtTGGgCDAY+FxG5zM9DVSepagNVbVC8ePG/f1bGmD/5+gh3Na5I1KA23NMshBmr9xLxxiKmLNvJudQ0yF8Cur5zob5u9iCY2By2LfB26MYYc03JyoQujguragDlgP0Z9JmjqgmqegRYAtQBUNUPVDVcVVsBx4BYtzFfq2MVkAYUu8zPM8ZkgYJB/ozoWpM5j7WkTvlCvPjDRjq/s5Slsa5V8FK14J6Z0P0z5xVin94GU++Aw1u9G7gxxlwjsjKhWw1UFpFQEckDdAe+T9fnO5ztUz/X1mpjYBOAiJRwfa0A3IpzwwPAt0Bb17EqQB7giGvu7iISICKhQGVgVRaenzEmncolg/n4vkZM7t2A5NQ07v5gFQ/8bw27jyY49XXVujj1dR1Gwp6VMKEp/DgEzhzzdujGGJOjZelz6ESkMzAG8AWmqOrLItIfQFUnuvoMBu7FWWl7X1XHuNqXAkWBc8CTqvqTqz0PMAWoi3MH7CBVXeg69ixwH8727OOq+uOl4rO7XI3JOkkpqUxZtotxC2M5l6rc3zKUAW2uJ3+A6/l0pw9D1CiI/ggCC0LEM9DgXvD192rcxhiTXdmDhT2whM6YrHfwVCKvzdnM12v3USI4gKcjq9GtXll8fFxlrwdjnLtgdy6GYlWh4yio3M67QRtjTDbktQcLG2NMyQKBjL6zLt883IzShfLy1BfruXXCcn7d43qMScma0Ps76D4N0s7B1Nvg09vh8BbvBm6MMTmIrdDZCp0xV01amvLNr/t4dc5mDscncVt4OZ6OrEqJAoFOh5RkWDUJFr8Oyaeh4QMQMQSCing3cGOMyQZsy9UDS+iM8Y7TSSmMW7iNKct24u8rPNK2Mve1CCHAz9fpkHAEFo2C6A8hoABEDIWG91t9nTEmV7OEzgNL6Izxrl1HEnh59ibmbzxIxaJBDOtSg3bVSzivEQM4uBHmDoUdUVCsiqu+rr1XYzbGGG+xGjpjTLYUUiwfk3s34JP7G+Hv60Pfj9fQe8oqYg/GOx1K1oC7v4UeM0DTYOrt8MmtcGizdwM3xphsxlbobIXOmGzhXGoan67czdvzt5KQnMrdTSryRLsqFAxybbOmJMPq92Hxq5B0Ghrc52zF5ivq3cCNMeYqsS1XDyyhMyb7OXo6idHztzJt1R4K5vXnqQ5V6dGoAr7nH3OScBSiXoE1UyAgv6u+7gGrrzPGXPMsofPAEjpjsq+Y/Sd5YeZGVu08RvXSBRjRtQZNKrmtxh3aBHOfge0LoWhl6PgyVO7gvJHCGGOuQVZDZ4zJcWqWKciMB5vwXs9wTp09R/dJKxkwdS1xx884HUpUh15fQ88vnJ8/uxM+vdVJ9IwxJpexFTpboTMm2zubnMqkJTuYsHgbqtCv9XU81Po68uZxPeYk9ZxTXxf1CiTFu+rrnrH6OmPMNcW2XD2whM6YnGXfibO8MnsTP/x2gDIFAxnauTo31i594TEnZ445Sd3qDyBPfoh4Ghr2Bb883g3cGGOuAEvoPLCEzpicadXOYzz/fQwbD5yiUUgRhnetQVjZghc6HNoM856FbQugyHVOfV2VSKuvM8bkaJbQeWAJnTE5V2qa8vmavbwxdwvHzyTTvWEFBnWoQtH8ARc6xc53bpw4shUqRTgPJi5Z01shG2PMv2IJnQeW0BmT8508e453FsTy8Ypd5M3jy+PtqtC7aUX8fV33fKWecx5xsmgUJJ2C+vdCm2cgXzGvxm2MMX+XJXQeWEJnzLVj26F4XvxhE0u2Hua64vkY3rUmrasUv9DhzDFY/BqsmuzU17UeDI36WX2dMSbHsITOA0vojLm2qCoLNx/ipR82suvoGdpVL8GzXWoQWizfhU6Ht8C8YRA7D4pUgg4vQ9VOVl9njMn2LKHzwBI6Y65NSSmpfPTzLt5duI2klFTuax7KI22vJzjQ7W0SsQtc9XVbILS1U19XKsx7QRtjTCYsofPAEjpjrm2H4hN5Y84WvoiOo1j+AP4vsiq3h5fD5/xrxFLPQfRHsOhlSDwJ4fdAm2chf/FLzmuMMd5gCZ0HltAZkzus33uC52fG8OueE9QpV5ARN9UkvELhCx3OHofFr8OqSeAfBK0GQ+N+4BfgeVJjjLnKLKHzwBI6Y3KPtDTlu/X7ePXHzRw8lUS3emUZ0qkaJQsEXuh0JBbmPguxc6FwKHQYCdW6WH2dMSZbsITOA0vojMl9EpJSGB+1jclLduLnKwxocz33twgl0N/3QqdtC5zE7vBmCGkJka9AqVreC9oYY7CEziNL6IzJvfYcPcPIWRuZt/EgFYoE8WyX6nSoUfLCa8RSUyD6Q+f5dWePQ3hvaPuc1dcZY7zGEjoPLKEzxiyLPcKLP8Sw9eBpml9flBFda1KlZPCFDmePw+I3YNV/wS+v8/y6xv2tvs4Yc9VZQueBJXTGGICU1DSm/rKH0fO3cjophV6NK/BE+yoUCnJ76PCRbc7z67b+CIVDXPV1N1p9nTHmqrGEzgNL6Iwx7o4lJDN6/hY++2UPBfP682SHqvRoWB6/868RA9i+0KmvO7TRqa/rOApK1/Ze0MaYXONSCZ1PRo0ZTPCYiBQQxwcislZEOlzZMI0xxruK5MvDyFtqMWtgS6qWCua5bzdw47vLWLH96IVO17WFfkuhy2gnqftvK/j+UTh9yHuBG2NyvctK6ID7VPUU0AEoDtwLvJplURljjBdVL12AaX2bMOGucOITU+gxeSUPT41m77EzTgdfP2h4Pzy6FpoOgHXTYGw4LHsbziV6N3hjTK50uQnd+SKRzsCHqrrerc0YY645IkKnWqX56anWPNm+Cgs3H6Ld6MWMnreFM8kpTqe8haDjyzDgFwhtBQueh/cawcbvIBeXsxhjrr7LqqETkQ+BskAoUAfwBaJUtX7Whpe1rIbOGHO59p84y2tzNvPduv2UKhDI0M7VuKlOmQuPOQHYEQVzhjpbsRWbO8+vK13HazEbY64t/7qGDrgfGAI0VNUzgD/OtmtmHxwpIltEZJuIDPHQJ0JE1olIjIgsdmt/TEQ2uNofd2t/XkT2ucasE5HOrvYQETnr1j7xMs/NGGMyVaZQXt7pXo8v+zelWHAeHpu+jjsmruD3uJMXOlWKcOrrbnzbeSjxf1vDdwMg/qC3wjbG5BKXu0LXHFinqgki0gsIB95R1d2XGOMLbAXaA3HAaqCHqm5061MIWA5EquoeESmhqodEJAyYDjQCkoE5wEOqGisizwOnVfXNdJ8XAvygqmGXe/K2QmeM+SdS05Qvo/fyxtwtHE1I5s765RkcWZVi+d2eTZd4Epa8ASsnOs+sa/kkNBkA/oGeJzbGmEu4Eit0E4AzIlIH+D9gN/BxJmMaAdtUdYeqJuMkaDen69MT+FpV9wCo6vnbxKoDK1X1jKqmAIuBbpcZqzHGZClfH+E/DSuwcFAED7QI5au1cbR5I4rJS3aQnJLmdAos6DyrbsAvzsrdTy/Cew0h5hurrzPGXHGXm9ClqLOUdzPOytw7QHAmY8oCe91+jnO1uasCFBaRKBGJFpHervYNQCsRKSoiQTg3Y5R3G/eIiPwmIlNEpLBbe6iI/Coii0Wk5WWemzHG/CMFAv15tksN5j7RivohhXl59iYi31nCoi1ujzApeh10nwq9v4eAAvBFH/iwE+z/1WtxG2OuPZeb0MWLyFDgbmCWazvVP5MxGd0Fm/5/S/2A+kAXoCPwnIhUUdVNwGvAfJzt1vWA67YyJgDXAXWBA8BbrvYDQAVVrQc8CXwmIgX+EpTIgyKyRkTWHD58OJNTMMaYzF1XPD8f3duID/s0BIV7P1zNvR+uYsfh0xc6VWoN/ZZA17FwdBtMioBvHoJTB7wWtzHm2nG5Cd1/gCSc59H9gbPS9kYmY+K4eFWtHLA/gz5zVDVBVY8AS3DuokVVP1DVcFVtBRwDYl3tB1U1VVXTgMk4W7uoapKqHnV9Hw1sx1kBvIiqTlLVBqraoHhxe8m2MebKaVOtBHMeb8WznauzetdxOo5ZwsuzNnIq8ZzTwccX6t/jPL+u+eOw4Ut4NxwWvw7JZ7wbvDEmR7ushM6VxE0FCorIjUCiqmZWQ7caqCwioSKSB+gOfJ+uz3dASxHxc22tNgY2AYhICdfXCsCtwDTXz6XdxnfD2Z5FRIq7Vg4RkUpAZWDH5ZyfMcZcKXn8fOjbqhKLBkXQrV5Z3l+2k7ZvRv1/e/cdZlV1vn38+zDD0HvvvQyIKE1FQJAqRRKjiaKx/5QEEks0ERQQFLFGjd3Ye2xJBJUqTRFpAsIMHYSh987U5/3jHN8McPaIypwz5f5cl5ecxdrnPOvaU27W3nst3p+/iays8EWK4mWh52gYMg+a9ITpY+HpdrD0A91fJyI/y6lu/fVbYB5wGfBb4BszuzSnY8IPMwwFJhEKae+7+3IzG2xmg8N9kgldUl0afv+X3H1Z+C0+MrMkYDwwxN33htsfNrPvzGwp0A24LdzeBVhqZkuAD4HB7r7nVMYnInK6VSlTjIcvbc1/h5xPvUql+OtHSxn4zFcs/D7bj6WKDeC3b8C1n0GpyvDxjfByT9g0P3aFi0i+dKrLliwBev7wFKqZVQGmunu+XjFTy5aISDS4O58s2cK4z1aw7cAxBp5Vk7suak6NciX+1ykrC5a+B1NHw6Ft0Ooy6D4KytcJfmMRKVRyWrbkVAPdd+7eKtvrIsCS7G35kQKdiETTkbQMnpuxlhdmrSPOjD90bcRNXRpSvGjc/zqlHoKvnoA5T4Ved/wznH8LFCsdm6JFJM84HYHuEeBMwvexEXpIYqm7/+20VRkDCnQiEgub9hxh3OfJfPbdNmqVL8Hwvon0bVX9+G3E9m0K7Q277EMoXR16jIIzL4cip/osm4gUNL840IXf5DfA+YSWI5nl7v8+fSXGhgKdiMTS12t3M3r8clZsO0iHBhUZNaAFLWuWO77Tpnmh/WE3L4AaZ0GfB6HeebEpWERi6rQEuoJIgU5EYi0zy3lv/kYenbSS/UfT+V37utzRqymVsm8jlpUFyz6CqaPgwGZoMRB6joEK9WNWt4hE388OdGZ2kJMXA4bQLJ27+0kL9+YnCnQiklfsP5LOk9NW88bXGyiREMct3Ztw9Xn1SYjPdok17Qh8/TR8+ThkZcC5f4TOfwktgyIiBZ5m6AIo0IlIXrNmx0HGTEhm1qqdNKxSipH9W9C1WdXjOx3YEtobdsm7UKoKXDgCzr4qtHCxiBRYCnQBFOhEJC9yd6av3MF9E5JZv+swFzavyj39EmlY5YQnXTcvhInDYdNcqNYKeo8NbTEmIgWSAl0ABToRycvSMrJ4fc4Gnpy2mmPpmVx3fn3+1L0JZYtn20rbHZL+A5NHwv6N0Kwf9LoPKjWKXeEikisU6AIo0IlIfrDzYCqPTlrJ+ws3UbFkAnf2bsZl7eoQVyTbMifpx2DuszD7MchIhXNuhi53QonysStcRE4rBboACnQikp8s27yf0eOXM3/DXlrWLMuoAS3p0KDi8Z0Obocv7oNv34KSFaHbcGhzLcTFx6RmETl9FOgCKNCJSH7j7oxfupVxnyWzdf8x+p9Zg2F9E6lVvsTxHbcuhUnDYcNsqJIIve+Hxj1iU7SInBYKdAEU6EQkvzqalsnzM9fy/My1mMHNXRox+IJGlEjI9qSrO6z4FCbfA3vXQ5Ne0GssVGkau8JF5GdToAugQCci+d3mfUcZ91kyE5ZupWa54tzVN5EBZ9Y4fhuxjFSY9yLMfBjSDkP7G6HrXaFLsiKSbyjQBVCgE5GCYt76PYwev5zlWw7Qvn4FRg1oyRm1TthG7PAumP4ALHwVipWFrsOg/Q0QVzTym4pInqJAF0CBTkQKksws54MFm3hk0kr2HEnjd+3qcEfvZlTOgf5rTQAAIABJREFUvo0YwPak0P1166ZDpSbQ635o2huyz+qJSJ6jQBdAgU5ECqIDx9J5atpqXv1qAyWKxvHn7k24puMJ24i5w+rJMOlu2L0aGnaD3g9AtRaxK1xEcqRAF0CBTkQKsrU7DzH202S+WLGDBpVLMaJ/It2aVT3+/rrMdJj/MswYB6kHoO210O1uKFU5ZnWLSGQKdAEU6ESkMAhtI5bEup2HuaBpFUb0b0HjqidsI3ZkD8x8COb9ExJKhRYlPudmiC8W+U1FJOoU6AIo0IlIYZGe+b9txI6mZXL1efW5pUcTypU44YGInStDy5ysngwVGoS2EWveX/fXieQBCnQBFOhEpLDZdSiVxyav4r35G6lQMoG/9GrK5e3rHr+NGMCaqaH763augPqdQ/fX1TgzNkWLCKBAF0iBTkQKq+Vb9jN6fBLz1u8hsUZZRg1owbkNKx3fKTMDFr0GX4yFo3vh7KvgwhFQplpMahYp7BToAijQiUhh5u589t02Hvgsmc37jtKvVQ3uuqg5dSqWPL7j0X0w6xH45oXQPXWdb4dzh0DR4rEpXKSQUqALoEAnIgLH0jN5cdY6np2xBne4uUtDBndtRMmE+OM77l4LU0bCiglQri70HA0tf63760SiRIEugAKdiMj/bNl3lIcmruC/i7dQvWxxhvVtzsWtax6/zAnAupmh++u2fwd1zoU+46BWm9gULVKIKNAFUKATETnZgg17GD0+ie8276dtvQqMGtCCM2uXP75TViZ8+xZ8cR8c3gmtr4DuI6FszdgULVIIKNAFUKATEYksK8v5cGEKD09awe7DaVzapjZ39mlG1TIn3Dd37AB8+Xf4+hkoEg/n3wod/wQJJSO/sYj8bAp0ARToRERydvBYOk9/sYZXvlpPsfg4hl7YmOvOr0+x+LjjO+7dAFNGQdJ/oGwt6HEvnHEpFCkS4V1F5OdQoAugQCcicmrW7zrM2E+TmJq8g3qVSnJPvxb0SKx68v1138+BicNg62Ko1S50f12dDrEpWqSAySnQ6Z9OIiLyoxpULsVL17Tn9es7UDSuCP/3xgKufmUeq7cfPL5jvY7wf9PhV8/B/hR4uSd8eAPs2xSbwkUKCc3QaYZOROQnSc/M4q253/P4lFUcTsvk9+fW47YeTSlX8oRtxFIPwVdPwpx/hF53/FPoHrtipU9+UxH5UTGboTOzPma20szWmNldAX26mtliM1tuZjOztd9iZsvC7bdma7/XzDaHj1lsZn2z/d2w8GetNLPeuTk2EZHCqmhcEa47vwEz7uzGFR3q8MbXG+j66HTenPs9GZlZ/+tYrDRceDcMXQCJA0KLEz/VFr59G7KyAt9fRH66XJuhM7M4YBXQE0gB5gNXuHtStj7lgTlAH3ffaGZV3X2HmZ0BvAd0ANKAicAf3H21md0LHHL3R0/4vBbAu+FjagJTgabunhlUo2boRER+ueStBxg9fjlz1+2hefUyjOzfgo6NK5/ccdN8mHgXbF4ANVpD73FQ//zoFyyST8Vqhq4DsMbd17l7GqGANvCEPoOAj919I4C77wi3JwJz3f2Iu2cAM4Ff/8jnDQTec/dUd18PrAnXICIiuSixRlne/b9zef6qNhxKzWDQS98w+M2FbNpz5PiOddrDjVPhkpfg8G54rS+8f3XoCVkR+UVyM9DVArLfBZsSbsuuKVDBzGaY2UIzuzrcvgzoYmaVzKwk0Beok+24oWa21MxeMbMKP+HzMLObzGyBmS3YuXPnzx+diIj8f2ZGnzNqMPX2C7izdzNmrtpJ97/P5JFJKzicmpG9I5x5GQydD93uhtVT4On2oS3Fjh2I3QBE8rncDHSRNvc78fpuPNAW6Af0BkaYWVN3TwYeAqYQuty6BPjhJ8JzQCPgLGAr8NhP+Dzc/UV3b+fu7apUqfLTRiQiIjkqXjSOId0aM/2OrvRvVYNnpq+l26Mz+HhRCllZ2X4kJ5SEC/4Kf1oYWq/uqyfhqTaw8LXQLhQi8pPkZqBL4fhZtdrAlgh9Jrr7YXffBcwCWgO4+8vu3sbduwB7gNXh9u3ununuWcA/+d9l1VP5PBERiYLq5Yrz99+dxUd/6EiNcsW5/f0l/Ob5OSzetO/4jmVrwq+fCy11UqkxjL8FXugS2i9WRE5Zbga6+UATM2tgZgnA5cAnJ/T5L9DZzOLDl1bPAZIBzKxq+P91gUsIPfCAmdXIdvyvCV2eJfzel5tZMTNrADQB5uXKyERE5JS0rVeBf//xfB69rDUpe4/yq2e+4vb3F7P9wLHjO9ZqA9d9Dpe9DqkH4I2L4d1BsHttbAoXyWdydR268JIiTwBxwCvuPtbMBgO4+/PhPncC1wFZwEvu/kS4fTZQCUgHbnf3aeH2NwldbnVgA3Czu28N/93dwPWELs/e6u6f51SfnnIVEYmeQ6kZPDN9DS/PXk98nDGkW2Nu6NSA4kVP2EYs/RjMfRZmPwYZqdDhJrjgTihRIfIbixQS2vorgAKdiEj0fb/7MGM/TWZy0nbqVizJ3f0S6dWi2snbiB3cDtPvh0VvhsJct+HQ9jqIi49N4SIxpkAXQIFORCR2vly9izETlrNq+yHOb1yJkf1b0qx6mZM7bl0Kk4bDhtlQpTn0HguNe0S/YJEYU6ALoEAnIhJbGZlZvDNvI49NXsXBY+lcFd5GrEKphOM7usPKz2DS3bB3PTTuGQp2VZrFpnCRGFCgC6BAJyKSN+w9nMYTU1fx1jcbKV0sntt7NuXKc+oSH3fCs3sZqTDvRZj5CKQdgvY3QNdhULJibAoXiSIFugAKdCIiecvKbQcZM2E5X63ZTdNqpRnZvyWdmkTYRuzwLpj+ACx8FYqVgQvugvY3QnzCyX1FCggFugAKdCIieY+7MzlpO2M/TWbjniP0bFGNe/olUq9SqZM7b08K3V+3LryOXa+x0LR3aEcKkQJGgS6AAp2ISN51LD2TV75az9NfrCEj07m+UwOGXtiY0sVOeMrVHVZPDt1ft3s1NOwKvR+Aai1jUbZIrlGgC6BAJyKS920/cIyHJ67ko0UpVClTjL/1ac4lZ9eiSJETZuEy02HBK6FLsakHoM01of1iS2ubRykYFOgCKNCJiOQfizft495PlrN40z5a1y7HqItb0qZuhMWGj+yBmQ/B/JegaEnocgecMxjii0W/aJHTSIEugAKdiEj+kpXl/HfJZh78fAXbD6Ty67Nr8bc+zalervjJnXeugsn3wOpJUKE+9LofmvfX/XWSbynQBVCgExHJnw6nZvDcjLW8OHsdcWYM6daIGzs3PHkbMYA100L31+1MhnqdoM8DUKN19IsW+YUU6AIo0ImI5G+b9hzhgc+S+XzZNmpXKMHdfRPpc0b1k7cRy8yARa/D9LGhS7JnXwkXjoAy1WNTuMjPoEAXQIFORKRgmLN2F2PGJ7Fi20HObViRUQNaklij7Mkdj+6DWY/ANy+E7qnrdBucNwSKloh+0SI/kQJdAAU6EZGCIyMzi/fmb+KxySvZfzSdKzrU5S+9mlHxxG3EAHavhSkjYcUEKFcXet4LLS/R/XWSpynQBVCgExEpePYdSeOJqat5c+73lEqI47aeTbnq3HoUPXEbMYD1s2DicNj+HdQ5N3R/Xa220S9a5BQo0AVQoBMRKbhWbz/ImAlJzF69i8ZVSzOifwsuaBphTbqsTFj8Nky7Dw7vgDMvh+4joVyt6BctkgMFugAKdCIiBZu7My15B/d/msSG3UfokViVu/u1oEHlCNuIHTsAX/4dvn4WrAh0uhU6/hkSSka/cJEIFOgCKNCJiBQOqRmZvPbVBp76Yg2pGZlcf35oG7EyxYue3HnvBpgyCpL+A2VqQo97odVlUCTCJVuRKFKgC6BAJyJSuOw4eIxHJ63kg4UpVCqVwF97N+fStrVP3kYM4Ps5MHEYbF0MNdtAnweh7jnRL1okTIEugAKdiEjhtDRlH6PHJ7Hw+720qlWOUQNa0K5+xZM7ZmXB0n/BtNFwcCuc8ZvQjF35utEuWUSBLogCnYhI4eXufLJkC+M+W8G2A8e4uHVN7rqoOTXLR1iTLu0wfPVk6D+A84aG1rArVjq6RUuhpkAXQIFORESOpGXw/Iy1vDBrHWbwhwsac/MFAduI7dsUmq377gMoXS30NGzrQbq/TqJCgS6AAp2IiPwgZe8Rxn2+gk+XbqVW+RIM75tI31YRthED2DQfJg2DlPlQ/UzoMw7qd4p+0VKo5BTo9E8KERERoHaFkjwzqA3v3XQuZUsUZcg7i/jdi3NZvmX/yZ3rtIcbpsBvXg7tDftaP/jX72HP+ugXLoJm6DRDJyIiJ8nMcv41fxOPTl7J3iNpXN6+Lnf0akql0sVO7px2BL5+JrSGXVYGnPsH6HwHFI+wl6zIL6BLrgEU6EREJCf7j6bzj2mreX3OBkokxHFL9yZcfV59EuIjXOA6sBWmjYEl70DJynDhPdDmaigS4V48kZ9BgS6AAp2IiJyKNTsOcd+EJGau2knDKqUY0b8F3ZpVjdx58yKYNBw2fg1VW4b2h23YNZrlSgGle+hERER+gcZVS/P69R149dr24HDdq/O57tV5rN156OTOtdrAdZ/DZa9D2kF4YyC8cznsWhP9wqXQ0AydZuhEROQnSMvI4o2vN/Dk1NUcTc/k2o71+XOPJpSNtI1Y+jH45jmY9RhkHIUON8MFd0KJClGvW/I/XXINoEAnIiI/165DqTw2eSXvzd9ExZIJ3NG7Gb9tV4e4SNuIHdoBX9wPi94Ihbmuw6DddRAXIQSKBIjZJVcz62NmK81sjZndFdCnq5ktNrPlZjYzW/stZrYs3H5rhOPuMDM3s8rh1/XN7Gj4vRab2fO5NzIRESnsKpcuxrhLzmT80E40rFKKYR9/x4CnvuSbdbtP7ly6Klz8Dxg8G6q1hM/vhOc6wuop0S9cCqRcm6EzszhgFdATSAHmA1e4e1K2PuWBOUAfd99oZlXdfYeZnQG8B3QA0oCJwB/cfXX4uDrAS0BzoK277zKz+sAEdz/jVGvUDJ2IiJwO7s6EpVsZ91kyW/Yfo9+ZNRjeN5FakbYRc4eVn8Hke2DPOmjUHXqPhaqJ0S9c8pVYzdB1ANa4+zp3TyMU0Aae0GcQ8LG7bwRw9x3h9kRgrrsfcfcMYCbw62zHPQ78FSi814tFRCTPMDMGtK7JtL905dYeTZiWvJ0LH53B41NWcTQt88TO0Lwf/PEb6P0AbF4Qmq2bcBsc3hWbAUi+l5uBrhawKdvrlHBbdk2BCmY2w8wWmtnV4fZlQBczq2RmJYG+QB0AM7sY2OzuSyJ8ZgMz+9bMZppZ59M6GhERkR9RIiGOW3s0ZdpfutKrZXWenLaaCx+bwSdLtnDSFbH4BDhvCPx5MbS/ERa+Dv84G756EjJSYzMAybdyM9BFuCv0pBm1eKAt0A/oDYwws6bungw8BEwhdLl1CZARDnd3AyMjvPdWoK67nw3cDrxjZict021mN5nZAjNbsHPnzp85NBERkWC1ypfgqSvO5v2bz6NiqQT+/O63XPb813yXEmEbsZIVoe8j8Mevoe65MGUkPNMBkj4JXZ4VOQW5GehSCM+qhdUGtkToM9HdD7v7LmAW0BrA3V929zbu3gXYA6wGGgENgCVmtiH8novMrLq7p7r77vCxC4G1hGYAj+PuL7p7O3dvV6VKldM4XBERkeN1aFCRT4Z24qHftGLD7sNc/MyX/O3Dpew8GGEGrkozuPIDuOpjiC8B7/8eXusPWxZHv3DJd3LzoYh4Qg9FdAc2E3ooYpC7L8/WJxF4mtDsXAIwD7jc3Zdle0CiLjAZOM/d957wGRuAduGHIqoAe9w908waArOBVu6+J6hGPRQhIiLRcuBYOk9/sYZXv1pPsfg4/nRhY649vz7F4iNsDZaZAYteh+lj4cgeOGsQXDgCytaIfuGSZ8TkoYjwwwxDgUlAMvC+uy83s8FmNjjcJ5nQJdWlhMLcS+6+LPwWH5lZEjAeGHJimIugC7DUzJYAHwKDcwpzIiIi0VS2eFGG901k0q1dOKdBRcZ9voLej89iatL2k++vi4uH9jfAnxZBx6Gw9H14qi3MfBjSjsRmAJKnaWFhzdCJiEgMzFy1k/smJLFmxyE6N6nMiP4taFqtTOTOe9aF7q1LHg9la0GPe+GMS6GIdvAsTLRTRAAFOhERiaX0zCzemvs9j09ZxeG0TK46py639WxK+ZIJkQ/Y8CVMGg5bl0CtdtBnHNTpEN2iJWYU6AIo0ImISF6w53Aaj09ZxdvffE/ZEkW5vWdTBnWoS3xchBm4rCxY8i5MGwOHtkHLS6DnaChfN/qFS1Qp0AVQoBMRkbxkxbYDjBmfxJy1u2larTQj+7ekU5PKkTunHgqtWTfnH6HlTc4bAp1vh2IBl20l31OgC6BAJyIieY27MzlpO2M/TWbjniP0SKzGPf0SqV+5VOQD9qfA1NHw3ftQqip0HwFnXQlFIjw9K/maAl0ABToREcmrUjMyeeXLDTz9xWrSMrO4vlMDhnZrTJniRSMfkLIAJg6DlHlQvVVoW7EGXaJbtOQqBboACnQiIpLX7ThwjEcmreSDhSlULl2Mv/ZuxqVta1OkSIQNmdxh+ccwZRTs3wTN+kGv+6BSo+gXLqedAl0ABToREckvlqbsY/T4JBZ+v5czapVl1ICWtK9fMXLn9KPw9TPw5eOhfWE73AQX3AklKkS3aDmtFOgCKNCJiEh+4u6MX7qVcZ8ls3X/MfqfWYNhfROpVb5E5AMObocv7oNv3wqFuW7Doe11oYWLJd9RoAugQCciIvnR0bRMnp+5lhdmrcUdbr6gEYMvaEjJhICgtnVpaP26DbOhcjPoPRaa9Ixu0fKLKdAFUKATEZH8bPO+ozz4+QrGL9lCjXLFueui5lzcuiZmAffXrfwMJt8T2nmiUfdQsKuaGP3C5WdRoAugQCciIgXB/A17GD1+Ocs2H6BtvQqMGtCCM2uXj9w5Iw3m/xNmPgSpB0OXYLsNh1IB691JnqFAF0CBTkRECoqsLOfDhSk8PGkluw6lcmnb2vy1dzOqli0e+YDDu2HmgzD/ZUgoDV3ugHNuhvhi0S1cTpkCXQAFOhERKWgOHkvn6elreOXL9STEFWHohU24vlN9isUHLDS8c2XoMuzqyVChAfQcA4kDINJlW4kpBboACnQiIlJQbdh1mLGfJTMlaTt1K5bk7n6J9GpRLfL9dQBrpsKku2HnCqjXKXR/Xc2zolu05EiBLoACnYiIFHRfrt7FmAnLWbX9EB0bVWLkgBY0r142cufMDFj0Gkx/AI7sgbMGwYUjoGyNqNYskSnQBVCgExGRwiAjM4t35m3k71NWceBoOleeU4/bejalYqmEyAcc3QezH4W5z0NcAnS6DToOhaIB691JVCjQBVCgExGRwmTfkTSemLqaN+d+T6mEOG7r2ZSrzq1H0bgikQ/Ysw6mjITk8VC2NvS4F1pdqvvrYkSBLoACnYiIFEarth/kvglJzF69i8ZVSzOifwsuaFol+IANX8LEYbBtKdRqB33GQZ0O0StYgJwDXUAkFxERkYKqabUyvHF9B166uh0ZmVlc88o8bnhtPut2Hop8QP1OcNNMGPgs7E+Bl3vCh9fDvo3RLVwCaYZOM3QiIlKIpWZk8vqcDfxj2hpSMzK5tmN9/tS9CWWLFw044BB89STM+Ufo9XlDQvfYFSsTvaILKV1yDaBAJyIiErLzYCqPTV7JvxZsomLJBO7o3YzftqtDXJGA++X2p8DU0fDd+1C6Glx4D5x1JRQJWO9OfjEFugAKdCIiIsdbtnk/o8cvZ/6GvbSoUZZRA1pwTsNKwQekLAjdX5cyD6q3gt4PQIMu0Su4ENE9dCIiInJKzqhVjvdvPo+nB53N/qPp/O7Fufzx7YVs2nMk8gG128ENk+E3L4eWO3l9ALx3JexeG93CCznN0GmGTkREJKJj6Zm8OGsdz85YQ5bDTZ0b8oeujShVLD7yAelH4etn4MvHISM1tDdslzuhRPnoFl5A6ZJrAAU6ERGRH7dl31EemriC/y7eQrWyxbjrouYMbF2LIkH31x3cDl/cB9++BSUqQLfh0PY6iAsIgnJKFOgCKNCJiIicuoXf72H0+CSWpuznrDrlGTWgBWfXrRB8wNalMGk4bJgNlZuF9odt0jN6BRcwCnQBFOhERER+mqws5+NvN/PQxBXsPJjKJWfX4m8XNada2eKRD3CHlZ/B5HtCO0806h4KdlUTo1t4AaBAF0CBTkRE5Oc5lJrBs9PX8NLs9cTHGUO6NeaGTg0oXjRg2ZKMNJj/T5jxEKQdgrbXhi7Flqoc1brzMwW6AAp0IiIiv8zG3Ud44LNkJi7fRu0KJbi7byJ9zqiOBe33eng3zBgHC16BhNLQ5Y7QwxPxxaJbeD6kQBdAgU5EROT0mLN2F2PGJ7Fi20HOaVCRUQNa0qJm2eADdqwIXYZdMwUqNIBe90Hz/hAUBCV269CZWR8zW2lma8zsroA+Xc1ssZktN7OZ2dpvMbNl4fZbIxx3h5m5mVXO1jYs/Fkrzax37oxKRERETtSxUWUm/KkT9//qDFZtP0j/p2Yz/N/fsftQauQDqjaHqz6Eqz4Kzc796yp4rT9sXRLdwguIXJuhM7M4YBXQE0gB5gNXuHtStj7lgTlAH3ffaGZV3X2HmZ0BvAd0ANKAicAf3H11+Lg6wEtAc6Ctu+8ysxbAu+FjagJTgabunhlUo2boRERETr/9R9J5ctpq3vh6AyUS4rilexOuPq8+CfEB80iZGbDoNZj+ABzZE9pCrPsIKFM9mmXnebGaoesArHH3de6eRiigDTyhzyDgY3ffCODuO8LticBcdz/i7hnATODX2Y57HPgrkD2NDgTec/dUd18PrAnXICIiIlFUrmRRRg5owcRbu9CmbgXu/zSZPk/MYvqKHZEPiIuH9jfCnxZBx6Gw9F/wjzYw85HQYsXyo3Iz0NUCNmV7nRJuy64pUMHMZpjZQjO7Oty+DOhiZpXMrCTQF6gDYGYXA5vd/cQ52VP5PMzsJjNbYGYLdu7c+XPHJiIiIj+icdXSvH59B169tj0A1702n2tfnceaHYciH1CiPPS6H4bOg8YXwvT74al2sPSD0PInEig3A12kuxpPPBvxQFugH9AbGGFmTd09GXgImELocusSICMc7u4GRv7Mz8PdX3T3du7erkqVKqc8GBEREfl5ujWvysRbu3BPv0QWfr+XPk/MYsz4JPYfSY98QMWG8Lu34NpPoWRF+PhGeKkHbJoX3cLzkdwMdCmEZ9XCagNbIvSZ6O6H3X0XMAtoDeDuL7t7G3fvAuwBVgONgAbAEjPbEH7PRWZW/RQ/T0RERGIgIb4IN3ZuyIw7uvLb9nV4dc56uj46nbfmfk9mVsDsW/1OcNNMGPgs7N8EL/eED6+HfRujW3w+kJsPRcQTeiiiO7CZ0EMRg9x9ebY+icDThGbnEoB5wOXuvizbAxJ1gcnAee6+94TP2AC0Cz8U0RJ4h/89FDENaKKHIkRERPKe5Vv2M2Z8Et+s30Pz6mUYOaAFHRvlsMhw6iH46gmY81To9XlDoNNtUKxMdArOA2LyUET4YYahwCQgGXjf3Zeb2WAzGxzuk0zokupSQmHuJXdfFn6Lj8wsCRgPDDkxzEX4vOXA+0BS+D2H5BTmREREJHZa1izHezedy3NXtuFQagaD/vkNg99cyMbdRyIfUKw0XHgPDF0AiQNg9mPwVFtY9CZk6de9FhbWDJ2IiEhMHUvP5KXZ63h2xloyspwbOzXgj90aU7pYfPBBKQtg4jBImQfVW0HvcdCgc/SKjgHtFBFAgU5ERCTv2Lb/GA9PXMHH326mapli/LVPcy45uxZFigTsHuEOyz6CqfeG7rFr3h96joFKjaJad7Qo0AVQoBMREcl7vt24l9Hjk1i8aR+ta5dj5ICWtK1XIfiA9KPw9TPw5eOQkRraG7bLnaFlUAoQBboACnQiIiJ5U1aW85/Fm3lo4gq2H0jlV2fV5G8XNadGuRLBBx3cDl/cB9++BSUqQLfh0Pa60MLFBYACXQAFOhERkbztcGoGz81Yy4uz1xFnxh+6NuKmLg0pXjQu+KCtS2HScNgwGyo3g95joUnP6BWdSxToAijQiYiI5A+b9hxh3OfJfPbdNmqVL8Gwvs3p16oGZjncX7fyM5h8D+xZB426h4Jd1cToFn4aKdAFUKATERHJX+au283o8Ukkbz1Ah/oVGTmgBWfUKhd8QEYazHsRZj4MaYeg7bWhS7GlcljzLo9SoAugQCciIpL/ZGY5/5q/iUcnr2TvkTR+164Of+nVjCpligUfdHg3zBgHC16BhNJwwZ3Q4SaIz+GYPEaBLoACnYiISP61/2g6T01bzWtzNlC8aBx/7t6Yazs2ICE+h30TdqwIXYZdMwUqNIBe94WWOwm6dJuHKNAFUKATERHJ/9buPMTYT5P5YsUOGlQuxd19E+meWDX4/jqANVNh0t2wcwXU6wR9HoAaraNX9M+gQBdAgU5ERKTgmLFyB/dNSGLtzsN0blKZkf1b0KRaDnu9ZmbAotdg+gNwZA+cdSV0HwFlqket5p9CgS6AAp2IiEjBkp6ZxVtzv+fxKas4nJbJ78+tx609mlC+ZELwQUf3wexHYe7zEJcAnW6DjkOhaA5r3sWAAl0ABToREZGCac/hNP4+ZSXvfLORsiWKcnvPpgzqUJf4uBzur9u9FqaMhBUToGxt6HEvtLo0z9xfp0AXQIFORESkYFux7QBjxicxZ+1umlYrzcj+LenU5EeWLFk/O7Qw8balUKsd9HkQ6rSPTsE5yCnQ5RBTRURERPK35tXL8vaN5/DC79tyLD2Lq17+hv97YwEbdh0OPqhBZ7hpBgx8BvZvgpd7wIc3wL5N0Sr7J9MMnWboRERECoVj6Zm88tV6nvliDemZznWd6jO0W2PKFC8afFD9Q1v1AAALzklEQVTqIfjqCZjzVOj1eUND99gVKx2dorPRJdcACnQiIiKFz44Dx3h40ko+XJhC5dLF+GvvZlzatjZFiuRwr9y+TTBtNHz3AZSuBheOgLMGQZEc9pQ9zRToAijQiYiIFF5LNu1j9PjlLNq4j1a1yjFyQAva16+Y80Gb5sOkYZAyH6q3gt7jQpdoo0CBLoACnYiISOHm7nyyZAsPfr6CrfuPMaB1Te66qDm1yuewZIk7LPsIpt4buseueX/oOQYqNcrVWhXoAijQiYiICMCRtAyen7mOF2auxQxu7tKIwRc0okRCDpdU04/C18/Al4+HZuuun5irNSrQBVCgExERkexS9h7hwc9XMGHpVmqUK85dFzXn4tY1c95G7OB2OLYPqjTL1dq0bImIiIjIKahdoSRPD2rD+zefR8VSCdzy3mIue/5rlqbsCz6oTLVcD3M/RoFORERE5AQdGlTkk6GdeOg3rdiw+zADn/mKOz9Ywo6Dx2JdWkQKdCIiIiIRxBUxfte+LtPv6MpNnRvyn8Wb6fbIDJ6bsZbUjMxYl3ccBToRERGRHJQpXpRhfROZfNsFnNeoMg9NXEGvx2cxafk28sqzCAp0IiIiIqegQeVSvHRNO968oQMJcUW4+c2FXPXyN6zcdjDWpSnQiYiIiPwUnZtU4fNbOjP64pYs23yAi56cxf0TkmJaU3xMP11EREQkH4qPK8I1HetzceuaPDF1FSVzWq8uGvXE9NNFRERE8rEKpRIYPfCMWJehS64iIiIi+V2uBjoz62NmK81sjZndFdCnq5ktNrPlZjYzW/stZrYs3H5rtvb7zGxp+JjJZlYz3F7fzI6G2xeb2fO5OTYRERGRvCLXLrmaWRzwDNATSAHmm9kn7p6UrU954Fmgj7tvNLOq4fYzgP8DOgBpwEQz+9TdVwOPuPuIcL8/AyOBweG3XOvuZ+XWmERERETyotycoesArHH3de6eBrwHDDyhzyDgY3ffCODuO8LticBcdz/i7hnATODX4T4Hsh1fCsgbC8CIiIiIxEhuBrpawKZsr1PCbdk1BSqY2QwzW2hmV4fblwFdzKySmZUE+gJ1fjjIzMaa2SbgSkIzdD9oYGbfmtlMM+t8ugckIiIikhflZqCzCG0nzqbFA22BfkBvYISZNXX3ZOAhYAowEVgCZPz/N3G/293rAG8DQ8PNW4G67n42cDvwjpmVPakos5vMbIGZLdi5c+cvGqCIiIhIXpCbgS6FbLNqQG1gS4Q+E939sLvvAmYBrQHc/WV3b+PuXYA9wOoIn/EO8Jtw/1R33x3+80JgLaEZwOO4+4vu3s7d21WpUuUXDVBEREQkL8jNQDcfaGJmDcwsAbgc+OSEPv8FOptZfPjS6jlAMkC2ByTqApcA74ZfN8l2/MXAinB7lfCDGJhZQ6AJsC6XxiYiIiKSZ+TaU67unmFmQ4FJQBzwirsvN7PB4b9/3t2TzWwisBTIAl5y92Xht/jIzCoB6cAQd98bbn/QzJqF+3/P/55w7QKMMbMMIBMY7O57cmt8IiIiInmFuRfeh0TbtWvnCxYsiHUZIiIiIj/KzBa6e7tIf6edIkRERETyOQU6ERERkXxOgU5EREQknyvU99CZ2U5CD1bktsrArih8Tl5UmMcOGr/GX3jHX5jHDhq/xp8746/n7hHXXCvUgS5azGxB0E2MBV1hHjto/Bp/4R1/YR47aPwaf/THr0uuIiIiIvmcAp2IiIhIPqdAFx0vxrqAGCrMYweNX+MvvArz2EHj1/ijTPfQiYiIiORzmqETERERyecU6HKRmfUxs5VmtsbM7op1PbnNzOqY2XQzSzaz5WZ2S7j9XjPbbGaLw//1jXWtucXMNpjZd+FxLgi3VTSzKWa2Ovz/CrGu83Qzs2bZzu9iMztgZrcW5HNvZq+Y2Q4zW5atLfBcm9mw8M+ClWbWOzZVnz4B43/EzFaY2VIz+7eZlQ+31zezo9m+Dp6PXeWnR8D4A7/eC9L5Dxj7v7KNe4OZLQ63F8RzH/S7Lqbf/7rkmkvMLA5YBfQEUoD5wBXunhTTwnKRmdUAarj7IjMrAywEfgX8Fjjk7o/GtMAoMLMNQDt335Wt7WFgj7s/GA72Fdz9b7GqMbeFv/Y3A+cA11FAz72ZdQEOAW+4+xnhtojn2sxaAO8CHYCawFSgqbtnxqj8Xyxg/L2AL9w9w8weAgiPvz4w4Yd+BUHA+O8lwtd7QTv/kcZ+wt8/Bux39zEF9NwH/a67lhh+/2uGLvd0ANa4+zp3TwPeAwbGuKZc5e5b3X1R+M8HgWSgVmyryhMGAq+H//w6oW/8gqw7sNbdo7Fod8y4+yxgzwnNQed6IPCeu6e6+3pgDaGfEflWpPG7+2R3zwi/nAvUjnphURJw/oMUqPOf09jNzAj9I/7dqBYVRTn8rovp978CXe6pBWzK9jqFQhRuwv8qOxv4Jtw0NHwZ5pWCeMkxGwcmm9lCM7sp3FbN3bdC6AcBUDVm1UXH5Rz/w7ywnHsIPteF8efB9cDn2V43MLNvzWymmXWOVVFREOnrvTCd/87Adndfna2twJ77E37XxfT7X4Eu91iEtkJxfdvMSgMfAbe6+wHgOaARcBawFXgshuXltvPdvQ1wETAkfGmi0DCzBOBi4INwU2E69zkpVD8PzOxuIAN4O9y0Fajr7mcDtwPvmFnZWNWXi4K+3gvT+b+C4/9BV2DPfYTfdYFdI7Sd9vOvQJd7UoA62V7XBrbEqJaoMbOihL7A33b3jwHcfbu7Z7p7FvBP8vGlhh/j7lvC/98B/JvQWLeH77n44d6LHbGrMNddBCxy9+1QuM59WNC5LjQ/D8zsGqA/cKWHb9IOX2raHf7zQmAt0DR2VeaOHL7eC8X5N7N44BLgXz+0FdRzH+l3HTH+/legyz3zgSZm1iA8a3E58EmMa8pV4XsnXgaS3f3v2dprZOv2a2DZiccWBGZWKnyDLGZWCuhFaKyfANeEu10D/Dc2FUbFcf86LyznPpugc/0JcLmZFTOzBkATYF4M6stVZtYH+BtwsbsfydZeJfywDGbWkND418WmytyTw9d7oTj/QA9ghbun/NBQEM990O86Yvz9H3+631BCwk95DQUmAXHAK+6+PMZl5bbzgd8D3/3wyDowHLjCzM4iNMW8Abg5NuXlumrAv0Pf68QD77j7RDObD7xvZjcAG4HLYlhjrjGzkoSe6s5+fh8uqOfezN4FugKVzSwFGAU8SIRz7e7Lzex9IInQpcgh+fUJxx8EjH8YUAyYEv4+mOvug4EuwBgzywAygcHufqoPFORJAePvGunrvaCd/0hjd/eXOfn+WSiA557g33Ux/f7XsiUiIiIi+ZwuuYqIiIjkcwp0IiIiIvmcAp2IiIhIPqdAJyIiIpLPKdCJiIiI5HMKdCIiMWBmXc1sQqzrEJGCQYFOREREJJ9ToBMRyYGZXWVm88xssZm9YGZxZnbIzB4zs0VmNs3MqoT7nmVmc8Obs//7h83ZzayxmU01syXhYxqF3760mX1oZivM7O3wCvQiIj+ZAp2ISAAzSwR+B5zv7mcRWun+SqAUoT1r2wAzCe0SAPAG8Dd3PxP4Llv728Az7t4a6Ehow3KAs4FbgRZAQ0Ir0IuI/GTa+ktEJFh3oC0wPzx5VoLQhttZ/G8D8reAj82sHFDe3WeG218HPgjv71vL3f8N4O7HAMLvN++HfS/DWwjVB77M/WGJSEGjQCciEsyA19192HGNZiNO6JfTHoo5XUZNzfbnTPQzWUR+Jl1yFREJNg241MyqAphZRTOrR+hn56XhPoOAL919P7DXzDqH238PzHT3A0CKmf0q/B7FzKxkVEchIgWe/jUoIhLA3ZPM7B5gspkVAdKBIcBhoKWZLQT2E7rPDuAa4PlwYFsHXBdu/z3wgpmNCb/HZVEchogUAuae05UCERE5kZkdcvfSsa5DROQHuuQqIiIiks9phk5EREQkn9MMnYiIiEg+p0AnIiIiks8p0ImIiIjkcwp0IiIiIvmcAp2IiIhIPqdAJyIiIpLP/T8CBXcjV9EHdQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# YOUR CODE HERE\n",
    "\n",
    "W, b = initialize(trainX.shape[1])\n",
    "training_loss_list, testing_loss_list = train(trainX, trainY, testX, testY, W, b, 200, 0.0001)\n",
    "prediction = predict(testX, W, b)\n",
    "accuracy_score(testY, prediction)  # 0.83625000000000005\n",
    "plot_loss_curve(training_loss_list, testing_loss_list)\n",
    "plt.title('learning rate:0.0001 epoch:200')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'learning rate:0.1 epoch:1000')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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11h6Pv+mmm2hsbNy/fM455+Tk/pUbNmxg+vTpvd5OPiicZSFSXApAS3N9yJWIiIj0D7kOZ4sXL2bw4MG5KK1gKZxlIRJLh7PWpsbD9BQRERGARYsWsW7dOmbPns0111wDwI033siJJ57IzJkzuf766wFoaGjg3HPPZdasWUyfPp17772X73//+2zevJkzzjiDM844A4BJkyaxY8cONmzYwNSpU7niiiuYNm0aCxYs2H+/zSVLljBz5kxOPvlkrrnmmsPOkDU3N3P55ZczY8YMjj/+eJ566ikAVqxYwbx585g9ezYzZ85kzZo1HdaZa7rOWRasJB3O2pq1W1NERPqhRxfBljdyu81RM+DsGzptvuGGG1i+fPn+K/I/8cQTrFmzhpdffhl35+Mf/zjPPPMM27dvZ8yYMTzyyCNA+p6bVVVVfPe73+Wpp55i2LBhh2x7zZo13H333dxxxx1ceOGFPPDAA1x66aVcfvnl3H777XzgAx9g0aJFh/0It9xyCwBvvPEGq1atYsGCBbz11lvcdtttfPWrX+Uzn/kMra2tJJNJFi9efEiduaaZsyxEi9PHnLUqnImIiPTIE088wRNPPMHxxx/PnDlzWLVqFWvWrGHGjBk8+eSTfP3rX+fZZ5+lqqrqsNuaPHkys2fPBuCEE05gw4YN7Nmzh7q6Oj7wgQ8AcMkllxx2O8899xyf/exnATj22GOZOHEib731FieffDL/8i//wne+8x3eeecdSktLe1RntjRzloWiknIAEgpnIiLSH3Uxw9VX3J1rr72Wq6666pC2ZcuWsXjxYq699loWLFjAdddd1+W2SkpK9r+ORqM0NTXRk3uGdzbmkksuYf78+TzyyCN89KMf5Uc/+hFnnnlm1nVmSzNnWSgqSc+cJVqaQq5ERESkf6isrKSurm7/8kc/+lHuvPNO6uvTJ9e9++67bNu2jc2bN1NWVsall17K1772NV555ZUOxx/OkCFDqKys5MUXXwTgnnvuOeyYU089lZ///OcAvPXWW2zcuJFjjjmG9evXc8QRR/CVr3yFj3/847z++uud1plLmjnLQlFwzFmyRTNnIiIi3VFdXc0pp5zC9OnTOfvss7nxxhtZuXIlJ598MgAVFRX87Gc/Y+3atVxzzTVEIhFisRg/+MEPALjyyis5++yzGT169P4D9Q/nxz/+MVdccQXl5eWcfvrph931+MUvfpGrr76aGTNmUFRUxF133UVJSQn33nsvP/vZz4jFYowaNYrrrruOJUuWdFhnLllPpv8K1dy5c33p0qV52/7bq15l8j2n8crcG5nzsSvz9j4iIiK5snLlSqZOnRp2GX2qvr6eiooKIH1Cwnvvvcf3vve9UGvq6Hcws2XuPrd9X82cZaGkNL1bM9mqS2mIiIgUqkceeYR//dd/JZFIMHHiRO66666wS8qKwlkWYvH0CQHepmPORERECtWnP/1pPv3pT4ddRo/phIAslJSmwxkKZyIiIpInCmdZiJem91+7dmuKiEg/MpCOL++Psv3+Fc6yECuK0uIxSDSHXYqIiEi3xONxdu7cqYAWEndn586dxOPxbo/RMWdZMDOaKcYS2q0pIiL9w7hx46ipqWH79u1hl/K+FY/HGTduXLf7K5xlqcVKiGjmTERE+olYLMbkyZPDLkOyoN2aWWq1YkzhTERERPJE4SxLrVZCNKlwJiIiIvmhcJalNoUzERERySOFsyy1RUqIpRTOREREJD8UzrKUiMYpSrWEXYaIiIgMUApnWUpGShTOREREJG8UzrKUjJZS7ApnIiIikh8KZ1lKRuMUe2vYZYiIiMgApXCWpVRRnBI0cyYiIiL5kddwZmYLzWy1ma01s0Wd9DndzF41sxVm9oeM9RvM7I2gbWk+68xKUZy4dmuKiIhInuTt9k1mFgVuAc4CaoAlZvawu7+Z0WcwcCuw0N03mtmIdps5w9135KvGHikqJWZJPNmGRWNhVyMiIiIDTD5nzuYBa919vbu3AvcA57XrcwnwS3ffCODu2/JYT27ESgFoa24MuRAREREZiPIZzsYCmzKWa4J1mY4GhpjZ02a2zMz+IqPNgSeC9Vd29iZmdqWZLTWzpdu3b89Z8Z0KwllzU0P+30tERETed/K2WxOwDtZ5B+9/AvBhoBR4wcxedPe3gFPcfXOwq/O3ZrbK3Z85ZIPutwO3A8ydO7f99nPOissAaG2qz/dbiYiIyPtQPmfOaoDxGcvjgM0d9HnM3RuCY8ueAWYBuPvm4Hkb8CDp3aShixSnZ85atVtTRERE8iCf4WwJMMXMJptZMXAR8HC7Pr8CPmRmRWZWBswHVppZuZlVAphZObAAWJ7HWrstGsyctbVot6aIiIjkXt52a7p7wsy+DDwORIE73X2FmV0dtN/m7ivN7DHgdSAF/Mjdl5vZEcCDZravxl+4+2P5qjUb0ZIgnOmYMxEREcmDfB5zhrsvBha3W3dbu+UbgRvbrVtPsHuz0BTFKwFoa6oLuRIREREZiHSHgCzFSisASDQrnImIiEjuKZxlqaR8EABJHXMmIiIieaBwlqWS0vRuzVSzLqUhIiIiuadwlqV4eRDONHMmIiIieaBwlqXy8kpSbtCmmTMRERHJPYWzLJXEojRSAq2aORMREZHcUzjLkpnRRBxrawq7FBERERmAFM56oMniRBOaORMREZHcUzjrgZZInGhCM2ciIiKSewpnPdBqZRQldONzERERyT2Fsx5oi8aJJRXOREREJPcUznqgLVpGLNUcdhkiIiIyACmc9UAiWkpJSseciYiISO4pnPVAsqiMuGvmTERERHJP4awHUrFy4iiciYiISO4pnPVErIw4rZBKhl2JiIiIDDAKZz3gxeUApFp0f00RERHJLYWzngjCWXPD3pALERERkYFG4awHoiVBOGvUzJmIiIjklsJZD0RKKgFoadTMmYiIiOSWwlkPFMXTM2cKZyIiIpJrCmc9UFSanjlra9JuTREREckthbMeiAXhLNGscCYiIiK5pXDWA8WlFYDCmYiIiOSewlkPlJQNAiClcCYiIiI5pnDWA6Xl6d2augitiIiI5JrCWQ/EyypIueGtDWGXIiIiIgOMwlkPlJXEaKQEa1M4ExERkdxSOOuBWDRCEyXQ1hh2KSIiIjLAKJz1UJPFiWjmTERERHIsr+HMzBaa2WozW2tmizrpc7qZvWpmK8zsD9mMDVOLxYkmNHMmIiIiuVWUrw2bWRS4BTgLqAGWmNnD7v5mRp/BwK3AQnffaGYjujs2bC1WSkzhTERERHIsnzNn84C17r7e3VuBe4Dz2vW5BPilu28EcPdtWYwNVUu0nFhS4UxERERyK5/hbCywKWO5JliX6WhgiJk9bWbLzOwvshgbqtZoOfGkrnMmIiIiuZW33ZqAdbDOO3j/E4APA6XAC2b2YjfHpt/E7ErgSoAJEyb0uNhstcYqibdo5kxERERyK58zZzXA+IzlccDmDvo85u4N7r4DeAaY1c2xALj77e4+193nDh8+PGfFH04qVkGpK5yJiIhIbuUznC0BppjZZDMrBi4CHm7X51fAh8ysyMzKgPnAym6ODVWquIJSWiCZCLsUERERGUDytlvT3RNm9mXgcSAK3OnuK8zs6qD9NndfaWaPAa8DKeBH7r4coKOx+aq1J7w4fX9NWvZC2dBwixEREZEBI5/HnOHui4HF7dbd1m75RuDG7owtJFZaBUBLYy0lCmciIiKSI7pDQA9F4oMAaKrbHXIlIiIiMpAonPVQUWk6nDXX7wm5EhERERlIFM56KFaW3q3ZXF8bciUiIiIykCic9VBJ+WAA2ho1cyYiIiK5o3DWQ8VBOEs27g25EhERERlIFM56qLQyCGfN2q0pIiIiuaNw1kMVFYNIupFqrgu7FBERERlAFM56qKI0Rj2l0KJwJiIiIrmjcNZDpbEo9ZRhLTrmTERERHJH4ayHzIxGKyXaWh92KSIiIjKAKJz1QpOVE00onImIiEjuKJz1QnO0nGKFMxEREckhhbNeaI2WU5JsCLsMERERGUAUznqhraiCkpTCmYiIiOSOwlkvJGMVlKYawy5DREREBhCFs15IFVdSSgskE2GXIiIiIgOEwlkveEll+kWrLkQrIiIiuaFw1htBOEs16f6aIiIikhsKZ70QLR0EQFP9npArERERkYFC4awXovEgnNXtDrkSERERGSgUznohWj4EgFbNnImIiEiOKJz1QnHFUABa63eGXImIiIgMFApnvRAfVA1AokG7NUVERCQ3FM56obwyPXOWbFQ4ExERkdxQOOuFqvI4e70MVzgTERGRHFE464VBpTH2eDnWrBMCREREJDcUznohHouy1yqItugitCIiIpIbCme91BipINamcCYiIiK5oXDWS03RSkra9oZdhoiIiAwQCme91BKrIp7Ujc9FREQkNxTOeqktNojyVB24h12KiIiIDAB5DWdmttDMVpvZWjNb1EH76WZWa2avBo/rMto2mNkbwfql+ayzN1IlVcRIQFtj2KWIiIjIAFCUrw2bWRS4BTgLqAGWmNnD7v5mu67PuvvHOtnMGe6+I1815oLH0/fXpGkPFJeHW4yIiIj0e/mcOZsHrHX39e7eCtwDnJfH9wuFlQ4GIKUL0YqIiEgO5DOcjQU2ZSzXBOvaO9nMXjOzR81sWsZ6B54ws2VmdmVnb2JmV5rZUjNbun379txUnoVoeXrmrHFvQU/wiYiISD+Rz3BmHaxrf9T8K8BEd58F/BfwUEbbKe4+Bzgb+JKZndrRm7j77e4+193nDh8+PBd1Z6WoIn1/zea9O/v8vUVERGTgyWc4qwHGZyyPAzZndnD3ve5eH7xeDMTMbFiwvDl43gY8SHo3acEpqawGoLluV8iViIiIyECQz3C2BJhiZpPNrBi4CHg4s4OZjTIzC17PC+rZaWblZlYZrC8HFgDL81hrj5UNSoezRL1mzkRERKT38na2prsnzOzLwONAFLjT3VeY2dVB+23ABcAXzCwBNAEXubub2UjgwSC3FQG/cPfH8lVrb1QMGkLSjYROCBAREZEcyFs4g/27Khe3W3dbxuubgZs7GLcemJXP2nJlUFkJtZTjCmciIiKSA7pDQC9Vlcao9XKseU/YpYiIiMgAoHDWS+XFUfZSQbSlNuxSREREZABQOOslM6MhUkmsTeFMREREek/hLAcaolXE27RbU0RERHpP4SwHmmKDKU8onImIiEjvKZzlQHPJUEq9Cdqawy5FRERE+jmFsxxIlaYvREuj7q8pIiIivaNwlgtlQThrUDgTERGR3lE4y4FoRfqG621120OuRERERPo7hbMcKBmUDmeNe7aGXImIiIj0dwpnOVA6ZCQAzbXbQq5ERERE+juFsxyoqBpGwiO07VU4ExERkd5ROMuBoRVxdlNJql4nBIiIiEjvKJzlwJDyGDt9EDTuDLsUERER6ecUznJgSFkxu7ySomaFMxEREekdhbMciEUj7I1WUdyyO+xSREREpJ9TOMuRpqIhlOrm5yIiItJLCmc50lI8mPLUXkgmwi5FRERE+jGFsxxJxINbODXtCrcQERER6de6Fc7M7KtmNsjSfmxmr5jZgnwX15+47q8pIiIiOdDdmbPPufteYAEwHLgcuCFvVfVDkeD+mjQqnImIiEjPdTecWfB8DvATd38tY50A0coRALTu2RJyJSIiItKfdTecLTOzJ0iHs8fNrBJI5a+s/ic+eAwAjbvfC7kSERER6c+KutnvL4HZwHp3bzSzoaR3bUqgfPAwWjxG2553wy5FRERE+rHuzpydDKx29z1mdinwDaA2f2X1P0MritlOFam92q0pIiIiPdfdcPYDoNHMZgF/B7wD/DRvVfVD1eUlbPPBWP3WsEsRERGRfqy74Szh7g6cB3zP3b8HVOavrP5neGUJ23wIRY3bwi5FRERE+rHuhrM6M7sW+CzwiJlFgVj+yup/ykuK2BUZQmnL9rBLERERkX6su+Hs00AL6eudbQHGAjfmrap+qrF4GKXJOmhrDrsUERER6ae6Fc6CQPZzoMrMPgY0u7uOOWuntTR9rTN03JmIiIj0UHdv33Qh8DLw58CFwEtmdkE+C+uPUuUKZyIiItI73d2t+Q/Aie7+f9z9L4B5wHLgOfIAACAASURBVD8ebpCZLTSz1Wa21swWddB+upnVmtmrweO67o4tRJFBo9Mv6nQ5DREREemZ7l6ENuLumach7uQwwS44aeAW4CygBlhiZg+7+5vtuj7r7h/r4diCUjI4Hc7a9r6nsyVERESkR7obzh4zs8eBu4PlTwOLDzNmHrDW3dcDmNk9pC/F0Z2A1ZuxoakYOoqkG027NiuciYiISI9094SAa4DbgZnALOB2d//6YYaNBTZlLNcE69o72cxeM7NHzWxalmMxsyvNbKmZLd2+PdzLWAwbVMYOqmjbsznUOkRERKT/6u7MGe7+APBAFtu2jjbTbvkVYKK715vZOcBDwJRujt1X1+2kgyNz587tsE9fSV+IdjCjdQsnERER6aHDHTdWZ2Z7O3jUmdnew2y7BhifsTwOOGhKyd33unt98HoxEDOzYd0ZW4j23SUg2qCzNUVERKRnupw5c/fe3KJpCTDFzCYD7wIXAZdkdjCzUcBWd3czm0c6LO4E9hxubCGqLi/hPR9KvGl92KWIiIhIP9Xt3ZrZcveEmX0ZeByIAne6+wozuzpovw24APiCmSWAJuCi4B6eHY7NV625UlwUYXdsBKWJWmhthOKysEsSERGRfiZv4Qz276pc3G7dbRmvbwZu7u7Y/qAxPiodM/e+C8OmhF2OiIiI9DPdvQitdFNrRXBSae2mrjuKiIiIdEDhLNcGjUs/19aEW4eIiIj0SwpnOVZaPZ6UG6k9CmciIiKSPYWzHBs5pIJtDKZl5zthlyIiIiL9kMJZjo2uKmWzV5PYrWPOREREJHsKZzk2qirOZh9GZK92a4qIiEj2FM5ybHRVnM1eTUnjFvBQ7yYlIiIi/ZDCWY4NLS9mqw2jKNUCjTvDLkdERET6GYWzHDMzmstGpxd0rTMRERHJksJZHiQrgwvR7lE4ExERkewonOVBdOik9Is9upyGiIiIZEfhLA8GDR1BrZfjuzaEXYqIiIj0MwpneTCmKs47PoLW7evCLkVERET6GYWzPBhVVcpGHwm73w67FBEREelnFM7yYHQwcxarq4FkIuxyREREpB9ROMuDsYNLecdHEvEE6E4BIiIikgWFszwYXBZje9GY9MIu7doUERGR7lM4ywMzIzl4YnpBx52JiIhIFhTO8qR06DhaKdLMmYiIiGRF4SxPxldXUuMjcM2ciYiISBYUzvJk/NAyNqRGkNixPuxSREREpB9ROMuT8UNLedtHE921DlKpsMsRERGRfkLhLE/GDyljnY8hkmzW5TRERESk2xTO8mTckDLWpoLLaWx/K9xiREREpN9QOMuT0uIou8snpxd2rA63GBEREek3FM7yqHLoKOoig2C7wpmIiIh0j8JZHk0YWsZ6Hws7tFtTREREukfhLI8mD6vgzcQoXDNnIiIi0k0KZ3k0eXg5a1NjsaZd0LAj7HJERESkH1A4y6MjhpWz1semF7RrU0RERLohr+HMzBaa2WozW2tmi7rod6KZJc3sgox1G8zsDTN71cyW5rPOfJk8rJw1qSCcbVsZbjEiIiLSLxTla8NmFgVuAc4CaoAlZvawu7/ZQb/vAI93sJkz3L3f7g8sLykiVTmWpmQFpVtXhF2OiIiI9AP5nDmbB6x19/Xu3grcA5zXQb//CzwAbMtjLaE5YkQF66KTYMsbYZciIiIi/UA+w9lYYFPGck2wbj8zGwucD9zWwXgHnjCzZWZ2Zd6qzLMjhpfzWtt4fOsK3WNTREREDiuf4cw6WOftlm8Cvu7uyQ76nuLuc4CzgS+Z2akdvonZlWa21MyWbt++vXcV58ERwyp4tW081tYAu98OuxwREREpcPkMZzXA+IzlccDmdn3mAveY2QbgAuBWM/sEgLtvDp63AQ+S3k16CHe/3d3nuvvc4cOH5/YT5MDk4eW8mZqYXtCuTRERETmMfIazJcAUM5tsZsXARcDDmR3cfbK7T3L3ScD9wBfd/SEzKzezSgAzKwcWAMvzWGveHDmsgrU+lpRFYWu//AgiIiLSh/J2tqa7J8zsy6TPwowCd7r7CjO7Omjv6DizfUYCD5rZvhp/4e6P5avWfBo3pJRIrJQdJRMYoZkzEREROYy8hTMAd18MLG63rsNQ5u6XZbxeD8zKZ219JRIxjh5ZwVuNkxXORERE5LB0h4A+cPTISl5qngB734W6LWGXIyIiIgVM4awPHDOqkuebJqUX3l0Wai0iIiJS2BTO+sAxoypZ4ZNIWRHU9Ms7UYmIiEgfUTjrA8eMqqSFYnZVHA3vKpyJiIhI5xTO+sDwihKGlhezJnY0vPsn3SlAREREOqVw1gfM0mdsvtx2BLTWwY63wi5JRERECpTCWR85dtQgHt8zLr1QsyTcYkRERKRgKZz1keljq1jZNoJkfAhsfDHsckRERKRAKZz1kRljq3AibB08B955LuxyREREpEApnPWRI4eXE49FeKNoGuzeALXvhl2SiIiIFCCFsz5SFI1w3OhB/K5pSnrFO38MtyAREREpSApnfWjG2CoWbx+GlwzSrk0RERHpkMJZH5oxbjD1rU7jyLmw4fmwyxEREZECpHDWh2aMrQJgfcUc2LlGx52JiIjIIRTO+tBRIyooL47yh9TM9Ip1vwu3IBERESk4Cmd9KBoxZk8YzOItQ6ByNKxVOBMREZGDKZz1sRMmDGHV1jraJp8B65+GZCLskkRERKSAKJz1sRMmDSXlsK7qJGjeA5tfCbskERERKSAKZ31s9vjBmMHTrdPAIrDmibBLEhERkQKicNbHqkpjHD2ikj++l4IJJ8OqR8IuSURERAqIwlkI5kwcwp/e2U3qmHNh25uwc13YJYmIiEiBUDgLwUlHDKWuJcHqIaemV6z6TbgFiYiISMFQOAvByUdWA/CHbWUwaqZ2bYqIiMh+CmchGFEZZ8qICv64bidM/Thsehlqa8IuS0RERAqAwllIPnBkNUve3kXr1E8CDq/fF3ZJIiIiUgAUzkJy8pHDaGpL8lrjEBg/H16/F9zDLktERERCpnAWkpOPqMYMnl2zA2Z+GravgvdeC7ssERERCZnCWUiqymLMmTCEp1dvg2nnQ7Q4PXsmIiIi72sKZyE689gRvF5Ty7ZEGUxZAG/cD8m2sMsSERGRECmchejMY0cA8NTqbXD8pdCwTZfVEBEReZ9TOAvRsaMqGVMV53crt6VnzgZPgJdvD7ssERERCVFew5mZLTSz1Wa21swWddHvRDNLmtkF2Y7tz8yMM6eO4Lm1O2hOAideAe88D1uWh12aiIiIhCRv4czMosAtwNnAccDFZnZcJ/2+Azye7diB4MPHjqSxNclLb+9K79osisOSO8IuS0REREKSz5mzecBad1/v7q3APcB5HfT7v8ADwLYejO33Tj6ymtJYlCdWbIGyoTDjz+G1e6FhZ9iliYiISAjyGc7GApsylmuCdfuZ2VjgfOC2bMdmbONKM1tqZku3b9/e66L7WjwW5cNTR/Do8i0kkik4+UuQaIIXbw27NBEREQlBPsOZdbCu/SXwbwK+7u7JHoxNr3S/3d3nuvvc4cOH96DM8P3ZrDHsamhN32tzxNT0/TZfvh2a9oRdmoiIiPSxfIazGmB8xvI4YHO7PnOBe8xsA3ABcKuZfaKbYweM044eTmVJEb9+LfiIp14DLXvhpR+GW5iIiIj0uXyGsyXAFDObbGbFwEXAw5kd3H2yu09y90nA/cAX3f2h7owdSOKxKAumjeKxFVtoSSRh9Ew45pz0rs3m2rDLExERkT6Ut3Dm7gngy6TPwlwJ3OfuK8zsajO7uidj81VrIfj47DHUNSf4w+rguLnTF6WD2bP/EW5hIiIi0qeK8rlxd18MLG63rv3B//vWX3a4sQPZB46sprq8mF++8i4Lpo2C0bNg1sXw4g9g7udgyKSwSxQREZE+oDsEFIhYNMKnThjHkyu3sq2uOb3yw/8IFoUn/ynU2kRERKTvKJwVkItOHE8i5dy/rCa9YtAYOOWrsOJBePuZcIsTERGRPqFwVkCOGF7B/MlDueflTaRSwZVDTvkqDJkMv/4qtDWFW6CIiIjkncJZgblk/gQ27mpMX/MMoLgMPv592LUenr4h3OJEREQk7xTOCsxHp41iSFmM/35hw4GVk0+F4z8Lf/wvqFkaVmkiIiLSBxTOCkw8FuXSkyby5MqtrN9ef6BhwT/DoLFw/+d07TMREZEBTOGsAP3FyZOIRSL86Lm3D6wsHQwX/Bhqa+A3fw3e4d2sREREpJ9TOCtAwytL+OScsTywrIYd9S0HGsbPgzP+HpY/oFs7iYiIDFAKZwXq8x86gpZEip/+ccPBDR/8GzjmXHj8Wlj3+1BqExERkfxROCtQR42oYOG0Udz5/AZ2N7QeaIhE4JM/hOFT4X8vg22rQqtRREREck/hrID9zYKjaWhN8MNn1h/cUFIJF98NRXH46Xmw6+2ONyAiIiL9jsJZATt6ZCXnzRrDXX98+8AtnfYZMhE++xAkW9IBbe/mcIoUERGRnFI4K3B/9ZGjaUs6N/9+7aGNI4+DSx+Axl1w18dgz8a+L1BERERySuGswE0aVs4l8ybw85c2smrL3kM7jD0hCGg74Mcf1TFoIiIi/ZzCWT/wN2cdTWW8iG8+/Cbe0fXNJsyHyxaDJ+EnC2HD831fpIiIiOSEwlk/MKS8mL9dcAwvrN/J4je2dNxp1HT43ONQVg0//Ti8dLsuVCsiItIPKZz1E5fMm8BxowfxzV+voLaxreNOQyfDFb+Hoz4Cj14DD30BWur6tlARERHpFYWzfiIaMf7tgpnsbGjl/z3yZucd41Vw0d1w2iJ47R647YOw6eW+K1RERER6ReGsH5k+toqrTzuC+5fV8NTqbZ13jETgjGvh8sWQSsGdH4XH/wFa6jsfIyIiIgVB4ayf+cqHpzBlRAV/d//rbK9r6brzxA/AF56D2Z+BF26GW+bBmw/rWDQREZECpnDWz5QURfmvS45nb1Mbf33vqyRThwla8So47+b0yQLxwXDfZ+G//ww2LembgkVERCQrCmf90LGjBvGt86bx3Nod3PJUBxen7ciEk+CqZ+Dsf4NtK+HHH4G7L4H3XstvsSIiIpIVhbN+6sK54zn/+LHc9ORb/OGt7d0bFC2C+VfBV1+DM74BG56FH56anklb81vt7hQRESkACmf9lJnxz5+YzrGjBvGln7/S8d0DOlNSAaddA3/1Bpz1LdixFn5+Adx6ErxwKzTszF/hIiIi0iXr8Irz/dTcuXN96dKlYZfRp7bUNvOJW54nYvDQl05hxKB49htJtMLyB2DJHfDuMogWwzHnwKyL4Mgzoagk94WLiIi8z5nZMnefe8h6hbP+b8XmWv78theYVF3OL66Yz+Cy4p5vbOub8Kf/SV8jrWkXFFfCMQvhuPPgyA9DcVnuChcREXkfUzgb4J55azuf/++lHDu6kv/5y/lUlcZ6t8FEK2x4BlY8BKt+A027IVoCE09Oz6YdeSaMnA5mufkAIiIi7zMKZ+8Dv1u5lat/toxpY6r46V/OY1C8lwFtn2QbbHgO1j4J634P24I7FJSPSN90ffxJMH4+jJ6pXaAiIiLdpHD2PvH4ii186eevcPTISu763ImMqOzBMWiHs3czrHsK1j8Nm16CPe+k10dLYMxsGD0rPas2agaMmAqx0tzXICIi0s8pnL2PPL16G1/8+StUVxTz08/NZ/Kw8vy+Yd1WqHk5HdQ2LYGty6E1uFWURaB6Cow8DqqPOvAYegSUDc1vXSIiIgUslHBmZguB7wFR4EfufkO79vOA/wekgATwV+7+XNC2AagDkkCio+LbUzg74LVNe7j8riWk3Ln54jl8cMqwvnvzVAp2v50OaVuWp5+3vQl7NoKnDvQrHQrVR8LgiVA1FqrGw6CxUDUu/SgdomPaRERkwOrzcGZmUeAt4CygBlgCXOzub2b0qQAa3N3NbCZwn7sfG7RtAOa6+47uvqfC2cE27Gjgyv9Zytpt9fzdwmO56tQjsDDDTqI1vQt059qMxzqo3QS170Kq7eD+sTKoGAkVI6B8+IFHxQgoH5Y+5q18OJQOTt+aqqgXZ6mKiIj0sc7CWVEe33MesNbd1wcF3AOcB+wPZ+5en9G/HBg4+1gLwKRh5Tz4xVP4uwde54ZHV/Hqxj3c8KkZvbvURm8UFcOwKelHe6kUNGyHvTVQW5MOa7U1UL8VGrbBrvWw8UVo3Emnf0yKSoOgVpUOa/Gq9GPfuuIKKC5Ph77i8q5fR3N0MoWIiEiW8hnOxgKbMpZrgPntO5nZ+cC/AiOAczOaHHjCzBz4obvfnsdaB6zykiJuvvh4Zo2r4t8eW82C/9zNv10wk9OPGRF2aQeLRKByZPox9oTO+6WS6YDWsB3qt0HDDmjeEzxqoSl4bq6F+i2wY/WBddlk/0gsfSJDtBiK4ulgWRQPlkvSj2jJgdeZbdHidLiLxCBSBJFo8FwUrM9Y7vARDfoFyxYFI338XuYDa7fO2j131reT11i73cjtZlk7aztkNraLtr6cud23V+CgvQPt1/mh/fu0TydjutxOF9vOS59e1NNZv9DaoNMVh3zmENsOac/H58/H+7VrD72tfdcsPkckCjMu6Hp7eZTPcNbR38KH/qfh/iDwoJmdSvr4s48ETae4+2YzGwH81sxWufszh7yJ2ZXAlQATJkzIWfEDiZlx5alH8oEjh/HX977KZT9ZwiXzJ/D1hcf2/npofS0STe/WrBgBI6d1f5w7tDVBawO0NUBrYyev9y3XQ6IFki3p50QLJJoh2XpguaXuwOtka7o9ETynEuDJ/H0PA1Jnoa6Lv0q6+stWRKSnikoHbDirAcZnLI8DNnfW2d2fMbMjzWyYu+9w983B+m1m9iDp3aSHhLNgRu12SB9zlssPMNBMH1vFr//vB/n3x1dz5/Nv88SKLfz9OVM5//ix4R6L1hfM0nc3KC4DhvfNe7qnZ/pSieDR1m45AcnEwcupZNAvo91TwYkUfuD1QQ8PHqnD9O2gX/u+mbUf/GE6fJn3/9vvsI7gz+r+P7Mdhbps+mRuv5NxHYXFPunTSc1djuvLPl3UmIuZ1ny3dVXnIYvZjMtFW7v2Pm+ji7befKdhtrVr7+rfvZD/TcxnOFsCTDGzycC7wEXAJZkdzOwoYF1wQsAcoBjYaWblQMTd64LXC4Bv5bHW9414LMo3PnYcnzh+LN94aDl/c99r3P3yRhadPZUTJg4Ju7yBxQyiRemHiIhIN0XytWF3TwBfBh4HVpI+E3OFmV1tZlcH3T4FLDezV4FbgE97+vTRkcBzZvYa8DLwiLs/lq9a34+mj63il1/4ADd8cgZv72jkUz/4I1f8dClvba0LuzQREZH3NV2EVmhoSfCT59/mh39YT31rgnNnjObq045k+tiqsEsTEREZsHSHADms3Q2t/PCZ9fz8xXeoa0lwylHVXHnqkXzoqGFEIgP8mDQREZE+pnAm3ba3uY27X9rInc+/zda9LUwYWsZF88ZzwQnj8nOvThERkfchhTPJWmsixaPL3+Pulzfy4vpdFEWMj0wdyXmzx3DGsSOIx6JhlygiItJvhXGHAOnniosinDd7LOfNHsu67fXcu2QTv3ylhsdWbKG8OMpHjhvJx2aO4dSjh1FSpKAmIiKSC5o5k6wkkileensXv3l9M48u38KexjbKiqOcctQwzjx2BKcfM5zRVaVhlykiIlLwtFtTcq4tmeK5tTv43cqtPLVqO+/uaQLg2FGVfODIYcw/YijzJw8N716eIiIiBUzhTPLK3VmzrZ6nVm3j6dXbeWXjbloSKczgmJGVnHRENcdPGMyscYOZWF028O9IICIichgKZ9KnWhJJXttUy0vrd/Li2ztZ9s5umtvStweqKo0xc1xV8BjMcaMHMXZwqS7XISIi7ysKZxKqtmSKt7bW8XpNLa/X7OG1TbWs3lpHMpX+81dWHGXKyEqOHlHBMaMqOXpkJVNGVjCyMq7QJiIiA5LCmRSc5rYkb763l9Vb6li9pY412+pYvaWeHfUt+/vEYxEmDC1jYnU5E4eWMXFY+nlSdTmjB8eJRfN2BzIREZG80qU0pODEY1HmTBjCnAkH33B9V0Mrb22tY822ejbubGDDzkY27mzk2TXb9+8ahfR9xUdUljCqqpQxVXFGVcUZXRVndFUpo4Pl4ZUlusyHiIj0KwpnUnCGlhdz0hHVnHRE9UHrUylnW10L7+xs4J2djdTsaWJLbRPv1TazZls9z7y1nYbW5CHbqywpYlhlCdXlxVRXFDOsooTqihKGBa+HlhdTVRrb/ygrjuqEBRERCY3CmfQbkYgxKpgRm98uuEH6jNG6lgRbapvZvKeJLbXN7KhvYUd9KzsbWtlR18LbOxpYumE3uxpb6WyPflHE9ge1QaUxBpfFDgpv5SVFlBdH088lRVTsfz6wrry4iKiOlRMRkR5QOJMBw8wYFI8xKB7j6JGVXfZNJFPsbmxjZ0MLO+tbqW1q6/jR2MbO+lbWb2+gtqmNvc1tnYa69uKxyP7gVhqLUhKLEi+KEI9FKY1FicfSr+OxKCWxSLDuQJ94Rp/iogjF0QjFRRFi0fTjwLIRC9pj0YhCoYhIP6dwJu9LRdEIwytLGF5ZktW4VMppakvS0JqgoSVJQ0uC+pZExnOSxtbMdek+zW1JmtqStLSl2N3YynttSZrbUgetb02mDl9AN0Qjlg5s0QOBbX+IC14XRYyiSIRIBIoi6UBXFLH0c9SIRiIHliNGJLM9cmh7NBr0s33LkWAZIpZeH4mkX5u1W7/vdYSgLb0umtk32Na+9nQbB213X3s06GMZ4yJmGICBkW4z0v3Tz+n17OvTSfu+vd3W1Xa0S1xEeknhTCQLkYjt33VJ15NzWUumnJbEwaGtOQhxrYkUbckDj5ZEirak719uTaTDXVsiY10yc5wH7en1yZSTSDrJlNOYSJB0SKZS+9clU05i/3PqoOX2r6Vj7YPbgXUWhMTOQx6Zyx0EQDKC4v73a/feB7cdvCKzvX2U7CpcHjSui/foujbrtK19MV3Vdmhbx7V0VE+PtnmY77S3cp3p8/K/CDkuMtc15rK8kqII91x5cu42mCWFM5ECEY0YZcVF9Ke7Xbm3D3KZAS5FytOzje6Qcg8ewTh3Uqn0+vbtKXdSqQN9Uwe1Hxh3uPZ9200Grz1dNJ5+wjNeA8FrDz4bOAfGZS7v++wdtR3yHmRuL2OdH3i/Lt+jk1ra/RIZv0n736h9zy76dnMcXY7zLtp6Nq79Cm/Xmjk0V5+3y++0fddeyvUlrfLxv0y5vupWoX+HxSFfpknhTER6zCy9G1RXKxERyR1dwVNERESkgCiciYiIiBQQhTMRERGRAqJwJiIiIlJAFM5ERERECojCmYiIiEgBUTgTERERKSAKZyIiIiIFROFMREREpIAonImIiIgUEIUzERERkQKicCYiIiJSQBTORERERAqIuXvYNeSMmW0H3snz2wwDduT5PSQ7+k0Kk36XwqTfpfDoNylMffG7THT34e1XDqhw1hfMbKm7zw27DjlAv0lh0u9SmPS7FB79JoUpzN9FuzVFRERECojCmYiIiEgBUTjL3u1hFyCH0G9SmPS7FCb9LoVHv0lhCu130TFnIiIiIgVEM2ciIiIiBUThrJvMbKGZrTaztWa2KOx63k/MbLyZPWVmK81shZl9NVg/1Mx+a2ZrguchGWOuDX6r1Wb20fCqH9jMLGpmfzKz3wTL+k1CZmaDzex+M1sV/Ddzsn6XcJnZXwd/dy03s7vNLK7fpO+Z2Z1mts3Mlmesy/p3MLMTzOyNoO37Zma5rlXhrBvMLArcApwNHAdcbGbHhVvV+0oC+Ft3nwqcBHwp+P4X8f/bu9cQK+o4jOPfpyzxkkWUUWuklXQlL0VIUkT2IiiyF0VSmkgQRNdXhVEEvepFRb0oE7oZSWamFEEXMjCCUtEssXoRFrVlGVTeIK9PL+YfnBZddu14ZtjzfGDZmd/ODHPOw875nfnPOQMrbU8EVpZ5yt9mARcA1wDPlQyj/e4DvmmZTyb1ewZ43/a5wCSqfJJLTST1APcCl9i+EDia6jlPJp33CtVz2upwclgA3AFMLD99t/m/pTkbmEuB72xvtr0HWALMrHmfuobtLbbXl+kdVC82PVQZLCqLLQJuKNMzgSW2d9v+HviOKsNoI0njgGuBF1rKyaRGksYAVwAvAtjeY/svkkvdhgEjJA0DRgK/kEw6zvYnwB99yoPKQdKpwBjbn7m6aP/VlnXaJs3ZwPQAP7XM95ZadJik8cAUYDVwiu0tUDVwwNiyWPLqjKeBB4ADLbVkUq8zgd+Bl8tw8wuSRpFcamP7Z+AJ4EdgC7DN9ockk6YYbA49Zbpvva3SnA3MwcaT8zHXDpM0GngLuN/29v4WPUgtebWRpOuArbbXDXSVg9SSSfsNA6YCC2xPAXZRhmkOIbkcYeUappnABOA0YJSk2f2tcpBaMum8Q+XQkXzSnA1ML3B6y/w4qtPS0SGSjqFqzBbbXl7Kv5VTzJTfW0s9eR1504HrJf1ANcx/laTXSCZ16wV6ba8u88uomrXkUp+rge9t/257L7AcuIxk0hSDzaG3TPett1Was4FZC0yUNEHSsVQXCb5T8z51jfJJmBeBb2w/1fKnd4C5ZXou8HZLfZak4ZImUF2wuaZT+9sNbM+3Pc72eKr/h49tzyaZ1Mr2r8BPks4ppRnA1ySXOv0ITJM0shzLZlBdN5tMmmFQOZShzx2SppU8b2tZp22GtXuDQ5HtfZLuBj6g+qTNS7Y31bxb3WQ6MAfYKGlDqT0EPA4slXQ71QHwJgDbmyQtpXpR2gfcZXt/53e7KyWT+t0DLC5vJDcD86jeiCeXGtheLWkZsJ7qOf6C6pvnR5NMOkrS68CVwEmSeoFHObxj1p1Un/wcAbxXftq7r7lDQERERERzZFgzIiIiokHSnEVEREQ0SErA4QAAAd5JREFUSJqziIiIiAZJcxYRERHRIGnOIiIiIhokzVlExP8k6UpJ79a9HxExNKQ5i4iIiGiQNGcR0TUkzZa0RtIGSQslHS1pp6QnJa2XtFLSyWXZyZI+l/SVpBXlHolIOlvSR5K+LOucVTY/WtIySd9KWly+PTwiYtDSnEVEV5B0HnAzMN32ZGA/cCswClhveyqwiupbwwFeBR60fRGwsaW+GHjW9iSqeyRuKfUpwP3A+cCZVHe2iIgYtNy+KSK6xQzgYmBtOak1guomxweAN8oyrwHLJR0PnGB7VakvAt6UdBzQY3sFgO2/Acr21tjuLfMbgPHAp0f+YUXEUJPmLCK6hYBFtuf/pyg90me5/u5p199Q5e6W6f3k+BoRhynDmhHRLVYCN0oaCyDpRElnUB0HbyzL3AJ8ansb8Keky0t9DrDK9nagV9INZRvDJY3s6KOIiCEv7+wioivY/lrSw8CHko4C9gJ3AbuACyStA7ZRXZcGMBd4vjRfm4F5pT4HWCjpsbKNmzr4MCKiC8ju7wx+RMTQJmmn7dF170dExL8yrBkRERHRIDlzFhEREdEgOXMWERER0SBpziIiIiIaJM1ZRERERIOkOYuIiIhokDRnEREREQ2S5iwiIiKiQf4BTmTLftDvkT8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# YOUR CODE HERE\n",
    "\n",
    "W, b = initialize(trainX.shape[1])\n",
    "training_loss_list, testing_loss_list = train(trainX, trainY, testX, testY, W, b, 1000, 0.1)\n",
    "prediction = predict(testX, W, b)\n",
    "accuracy_score(testY, prediction)  # 0.83625000000000005\n",
    "plot_loss_curve(training_loss_list, testing_loss_list)\n",
    "plt.title('learning rate:0.1 epoch:1000')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
